INABA Michiaki

モジュライ

代数幾何学

moduli

alagebraic geometry

Natural sciences, Algebra

2002, - 九州大学大学院数理学研究員助手

Comptes Rendus. Mathématique, Cellule MathDoc/CEDRAM, On the moduli spaces of framed logarithmic connections on a Riemann surface, Indranil Biswas; Michi-aki Inaba; Arata Komyo; Masa-Hiko Saito, 13 Jul. 2021, 359, 5, 617, 624, Scientific journal, 10.5802/crmath.199

Refereed, Bulletin des Sciences Mathématiques, Elsevier BV, Unfolding of the unramified irregular singular generalized isomonodromic deformation, Michi-aki Inaba, Dec. 2019, 157, 102795, 102795, Scientific journal, 10.1016/j.bulsci.2019.102795

Refereed, J. Math. Soc. Japan, Moduli of regular singular parabolic connections with given spectral type on smooth projective curves, Michi-aki Inaba; Masa-Hiko SAITO, 2018, 70, no. 3,, 879, 894, Scientific journal, 10.2969/jmsj/76597659

Refereed, Kyoto Journal of Mathematics, Moduli of unramified irregular singular parabolic connections on a smooth projective curve, Michi-Aki Inaba; Masa-Hiko Saito, In this paper we construct a coarse moduli scheme of stable unramified irregular singular parabolic connections on a smooth projective curve and prove that the constructed moduli space is smooth and has a symplectic structure. Moreover, we will construct the moduli space of generalized monodromy data coming from topological monodromies, formal monodromies, links, and Stokes data associated to the generic irregular connections.We will prove that for a generic choice of generalized local exponents, the generalized Riemann-Hilbert correspondence from the moduli space of the connections to the moduli space of the associated generalized monodromy data gives an analytic isomorphism. This shows that differential systems arising from (generalized) isomonodromic deformations of corresponding unramified irregular singular parabolic connections admit the geometric Painleve property as in the regular singular cases proved generally. © 2013 by Kyoto University., Jun. 2013, 53, 2, 433, 482, Scientific journal, 10.1215/21562261-2081261

Refereed, Journal of Algebraic Geometry, Moduli of parabolic connections on curves and the Riemann-Hilbert correspondence, Michi-Aki Inaba, Let (C, t) (t = (t1, . . . , tn)) be an n-pointed smooth projective curve of genus g and take an element λ = (λ(i) j ) ∈ Cnr such that - ∑ i,j λ(i) j = d ∈ Z. For a weight α, let Mα C (t,λ) be the moduli space of α-stable (t,λ)-parabolic connections on C and let RPr(C, t)a be the moduli space of representations of the fundamental group π1(C\\{t1, . . . , tn}, *) with the local monodromy data a for a certain a ∈ Cnr. Then we prove that the morphism RH : Mα C (t, λ) → RPr(C, t)a determined by the Riemann-Hilbert correspondence is a proper surjective bimeromorphic morphism. As a corollary, we prove the geometric Painlev́e property of the isomonodromic deformation defined on the moduli space of parabolic connections. © 2013 University Press, Inc., 2013, 22, 3, 407, 480, Scientific journal, 10.1090/S1056-3911-2013-00621-9

Refereed, ADVANCES IN MATHEMATICS, ACADEMIC PRESS INC ELSEVIER SCIENCE, Smoothness of the moduli space of complexes of coherent sheaves on an abelian or a projective K3 surface, Michi-aki Inaba, For an abelian or a projective K3 surface X over an algebraically closed field k, consider the moduli space Splcpx(X/k)(et) of the objects E in D(b)(Coh(X)) satisfying Ext(X)(-1) (E, E) = 0 and Hom(E, E) congruent to k. Then we can prove that Splcpx(X/k)(et) is smooth and has a symplectic structure. (C) 2011 Elsevier Inc. All rights reserved., Jul. 2011, 227, 4, 1399, 1412, Scientific journal, 10.1016/j.aim.2011.03.001

Refereed, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, MATH SOC JAPAN, Moduli of stable objects in a triangulated category, Michi-aki Inaba, We introduce the concept of strict ample sequence in a fibered triangulated category and define the stability of the objects in a triangulated category. Then we construct the moduli space of (semi) stable objects by GIT construction., Apr. 2010, 62, 2, 395, 429, Scientific journal, 10.2969/jmsj/06220395

Refereed, PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, KYOTO UNIV, Moduli of stable parabolic connections, Riemann-Hilbert correspondence and geometry of Painleve equation of type VI, Part I - Dedicated to Professor Kyoichi Takano on his 60th birthday, Michi-aki Inaba; Katsunori Iwasaki; Masa-Hiko Saito, In this paper, we will give a complete geometric background for the geometry of Painleve VI and Garnier equations. By geometric invariant theory, we will construct a smooth fine moduli space M-n(alpha)(t, lambda, L) of stable parabolic connections on P-1 with logarithmic poles at D(t) = t(1) +(...)+t(n) as well as its natural compactification. Moreover the moduli space R(P-n,P-t)(a) of Jordan equivalence classes of SL2 (C)-representations of the fundamental group pi(1) (P-1\D(t),(*)) are defined as the categorical quotient. We define the Riemann-Hilbert correspondence RH : M-n(alpha) (t, lambda, L) -> R (P-n.t)(a) and prove that RH is a bimeromorphic proper surjective analytic map. Painleve and Garnier equations can be derived from the isomonodromic flows and Painleve property of these equations are easily derived from the properties of RH. We also prove that the smooth parts of both moduli spaces have natural symplectic structures and R(P-n,P-t)(a) is a symplectic resolution of singularities of from which one can give geometric backgrounds for other interesting phenomena, like Hamiltonian structures, Backlund transformations, special solutions of these equations., Dec. 2006, 42, 4, 987, 1089, Scientific journal, 10.2977/prims/1166642194

Refereed, Moduli Spaces and Arithmetic Geometry (Kyoto, 2004), Mathematical Society of Japan, Moduli of stable parabolic connections, Riemann-Hilbert correspondence and geometry of Painlevé equation of type VI, part II, Michi-aki Inaba; Katsunori Iwasaki; Masa-Hiko Saito, 2006, 45, 387, 432, International conference proceedings, 10.2969/aspm/04510387

Refereed, Seminaires et Congres, Dynamics of the sixth Painleve equation, Michiaki Inaba; Katsunori Iwasaki; Masa-Hiko Saito, 2006, 14, 103, 167, International conference proceedings

Refereed, INTERNATIONAL MATHEMATICS RESEARCH NOTICES, HINDAWI PUBLISHING CORPORATION, Backlund transformations of the sixth Painleve equation in terms of Riemann-Hilbert correspondence, M Inaba; K Iwasaki; MH Saito, 2004, 1, 1, 30, Scientific journal

Refereed, JOURNAL OF ALGEBRAIC GEOMETRY, AMER MATHEMATICAL SOC, On the moduli of stable sheaves on some nonreduced projective schemes, M Inaba, We study the moduli space of stable sheaves on a projective scheme whose structure sheaf has a nilpotent ideal with some property. We introduce a stratification on this moduli space. Each stratum is the moduli space of some extensions of sheaves. This stratification is described on a curve with multiple structure and on a double plane, and the structure of each stratum is studied. In the case of a curve with multiple structure, we also study a local structure of the moduli space of stable sheaves., Jan. 2004, 13, 1, 1, 27, Scientific journal

Refereed, JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, KINOKUNIYA CO LTD, Toward a definition of moduli of complexes of coherent sheaves on a projective scheme, M Inaba, Oct. 2002, 42, 2, 317, 329, Scientific journal

Refereed, NAGOYA MATHEMATICAL JOURNAL, DUKE UNIV PRESS, On the moduli of stable sheaves on a reducible projective scheme and examples on a reducible quadric surface, M-a. Inaba, We study the moduli space of stable sheaves on a reducible projective scheme by use of a suitable stratification of the moduli space. Each stratum is the moduli space of "triples", which is the main object investigated in this paper. As an application, we can see that the relative moduli space of rank two stable sheaves on quadric surfaces gives a nontrivial example of the relative moduli space which is not flat over the base space., Jun. 2002, 166, 135, 181, Scientific journal

Refereed, JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, KINOKUNIYA CO LTD, Moduli of parabolic stable sheaves on a projective sheme, M Inaba, Feb. 2000, 40, 1, 119, 136, Scientific journal

Refereed, 京大・理4.19, 放物接続のモジュライとパンルベ第6方程式, 稲場道明, 2006

Michi-aki Inaba, Discussion Meeting on Bundles -2019, Unfolding of the unramified irregular singular generalized isomonodromic deformation, 25 Mar. 2019, 29 Mar. 2019

Michi-aki Inaba, "Quantum Fields, Geometry and Rep Theory" meeting at ICTS, Moduli space of regular singular parabolic connections and isomonodromic deformation, 16 Jul. 2018, 16 Jul. 2018, 27 Jul. 2018

Grant-in-Aid for Scientific Research (A), 01 Apr. 2022, 31 Mar. 2027, 22H00094, Algebraic Geometry and Integrable Systems -- Moduli theory and Equations of Painleve type, 齋藤 政彦; 山田 泰彦; 岩木 耕平; 望月 拓郎; 吉岡 康太; Rossman W.F; 稲場 道明; 光明 新, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Kobe Gakuin University, 41340000, 31800000, 9540000, kaken

Grant-in-Aid for Scientific Research (C), Apr. 2019, Mar. 2024, 19K03422, moduli space of connections and the generalized isomonodromic deformation, 稲場 道明, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Kyoto University, 2600000, 2000000, 600000, １．不分岐不確定接続のモジュライ空間上の一般モノドロミー保存変形のunfoldingの構成についての論文を完成させ、Bulletin des Sciences Mathematiquesに掲載された。射影直線上の不分岐不確定線形常微分方程式に対する一般モノドロミー保存変形は、神保・三輪・上野理論として広く知られている。これを一般種数の曲線上の不確定接続のモジュライ空間上にも拡張することができ、Boalch, Hurtubise, Inaba-Saitoなどの論文において、それぞれの文脈で構成されている。この一般モノドロミー保存変形は接続のモジュライ空間上で代数的な微分方程式を定めるが、その本来の意味は、不確定接続が定めるストークスデータ(一般モノドロミー)が一定になる部分と捉えられる。曲線上の因子の退化に対し、ストークスデータのunfolding理論がHurtubise, Lambert, Rousseauによって構築されていた。この理論に動機づけられて、確定から不確定に退化する接続のモジュライ空間の族の上で、不確定一般モノドロミー保存変形を確定接続のモジュライ空間上に拡張することを試みた。実際にはunfolded Stokes dataを一定に保つことはほぼ不可能で、因子の周りのある種のデータに応じて一般モノドロミー保存変形のunfoldingを構成する仕組みを作ることができた。今回の理論の整備に伴い、不分岐不確定接続のモジュライ空間上の一般モノドロミー保存変形が可積分条件を満たすことの見通しの良い証明も与えることができた副産物もある。 ２．frame付接続のモジュライ空間上のシンプレクティック構造と、モジュライ空間上の 大域的代数関数についての、Biswas氏、光明氏、齋藤氏との共同研究を始め、概ね結果が出て、現在原稿作成中である。, kaken

Grant-in-Aid for Scientific Research (C), 01 Apr. 2014, 31 Mar. 2019, 26400043, integrable system and moduli theory of derived category, Inaba Michiaki; Saito Masa-Hiko; Abe Takeshi; Mochizuki Takuro; Yoshioka Kota; Komyo Arata, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Kyoto University, 3250000, 2500000, 750000, I constructed the moduli space of irreuglar singular connections on algebraic curves. It was difficult to formulate the moduli of ramifeid irregular singular connections, but I succeeded in its formulation and proved that the moduli space of ramified irregular singular connections is smooth with a symplectic structure. On the other hand, the construction of the unramified irregular singular connections is rather easy and we can construct the generalized isomonodromic deformation based on the Jimbo-Miwa-Ueno theory on the unramified moduli spaces. I also constructed a deformation of the unramified moduli space to the regular singular moduli spaces and gave a local analytic lift of the generalized isomonodromic deformation., kaken

Grant-in-Aid for JSPS Fellows, 09 Nov. 2015, 31 Mar. 2018, 15F15318, Study on vector bundles and applications to stability and freeness of logarithmic vector fields along a hypersurface, 稲場 道明; PONS-LLOPIS JOAN FRANCISCO, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Kyoto University, 2300000, 2300000, Pons-Llopis氏は，自らのACM層の基礎的研究を発展させるために，Miro-Roig氏，Malaspina氏，Faenzi氏などとそれぞれコンタクトを取って共同研究を実行し，多くの研究成果を導いた． まず第一にBallico, Huh, Malaspinaとの共著論文で，重複度２重の射影平面上のACM層の分類を行った．さらにm重射影平面に拡張した場合に，階数１のUlrich層は直線束のテンソルを除いて重複度m-1の射影平面のイデアル層に限ることを示した．第二に，Aprodu, Huh, Malaspinaとの共著論文において，最小次数を持つ非特異射影多様体上のUlrichベクトル束の記述を行い，特に有理scroll上のUlrich束の分類的記述を行った．この研究結果を導く際に，連接層の導来圏のfull exceptional collectionに対するorthogonalcomplementの存在を用いるという導来圏の手法を使った見通しよい記述が出来ている．第三に，Miro-Roigとの共同研究で，種数２以上の楕円曲面上で，ある特別な安定Ulrichベクトル束の族の構成を行った．第四に，Malaspina, Marchesiとの共著論文として，特別な３次元Fano多様体である旗多様体F=F(0,1,2)上のインスタントンベクトル束の記述を，8c_2(E)-3次元の族として構成した．これのjumping conicのなすスキームはF上のヒルベルトスキーム上の因子として具体的に記述される．第五に，任意の射影多様体がACM層の台となるかという予想に関連して，Faenziとの共著論文において，射影空間内の可約かつ非退化なACM閉部分スキームが非有界な次元のACM層の族を持つための条件を分類，決定した．, kaken

Grant-in-Aid for Scientific Research (S), 31 May 2012, 31 Mar. 2017, 24224001, Developments in Interactions between Algebraic Geometry and Integrable Systems, Saito Masa-Hiko; NORO Masayuki; KOIKE Tatsuya; INABA Michi-aki; MORI Shigefumi; MUKAI Shigeru; IWASAKI Katsunori; KANEKO Masanobu; HARAOKA Yoshishige; NAMIKAWA Yoshinori; ISHII Akira; FUJINO Osamu; HOSONO Shinobu; MATSUSHITA Daisuke; ABE Takeshi; IRITANI Hiroshi; TODA Yukinobu; NAKAJIMA Hiraku; NAKAMURA Iku; TANIGUCHI Takashi; ONO Kaoru; ROSSMAN Wayne; MITSUI Kentaro; SANO Taro, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Kobe University, 123370000, 94900000, 28470000, We established the geometric Painleve property of nonlinear differential equations for isomonodromic deformations of connections with generic unramified irregular singularities and regular singularities with fixed spectral types. We also established theory of Mixed twister D-modules and developed several geometric theories for integrable systems. As for higher dimensional algebraic geometry, certain types of extremal contractions of 3-dimensinal terminal varieties were classified in detail. Fujino proved that canonical rings of compact Kahler manifolds are finitely generated. Several results for symplectic varieties, moduli theory were obtained in our research projects. Mathematical foundations of Quantum cohomology rings were developed by the group of Fukaya, Ono and others. Several developments of mirror symmetry, including the case of toric Calabi-Yau varieties, are obtained. We also obtained several important results on derived categories of sheaves on algebraic varieties., kaken

Grant-in-Aid for Scientific Research (A), 01 Apr. 2010, 31 Mar. 2015, 22244003, Constructions and developments of geomerty on moduli spaces and arithmetic varieties, MORIWAKI Atsushi; MUKAI Shigeru; NAKAJIMA Hiraku; NAMIKAWA Yoshinori; YOSHIKAWA Kenichi; MOCHIZUKI Takuro; YOSIOKA Kota; KAWAGUCHI Shu; FUJINO Osamu; ABE Takeshi; INABA Michiaki, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Kyoto University, 46930000, 36100000, 10830000, Our six teams made international and surprising progresses of constructions and developments on geometries on moduli spaces and arithmetic varieties. For example, Prof. Mochizuki, who is a member of this research project, was elected as a plenary speaker of Soul International congress of Mathematicians 2014. Moreover, we supported the intercity seminars between Paris, Barcelona and Kyoto by this project. We could produce a lot of significant international researches such as joint works of Moriwaki and H. Chen at Fourier Institute, Grenoble University., kaken

Grant-in-Aid for Scientific Research (S), 2007, 2011, 19104002, New developments and interaction between Algebraic Geometry and Integrable Systems, SAITO Masa-hiko; NOUMI Masatoshi; YOSHIOKA Kota; YAMADA Yasuhiko; OHTA Yasuhiro; YAMAKAWA Daisuke; FUKAYA Kenji; INABA Michiaki; TAKASAKI Kanehisa; MORI Shigefumi; MUKAI Shigeru; IWASAKI Katsunori; KANEKO Masanobu; HARAOKA Yoshishige; NAMIKAWA Yoshinori; ISHII Akira; FUJINO Osamu; HOSONO Shinobu; MATSUSHITA Daisuke; YOSHINAGA Masahiko; KOIKE Tatsuya; MOCHIZUKI Takuro; IRITANI Hiroshi; HARASHITA Shushi; TODA Yukinobu, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Kobe University, 99190000, 76300000, 22890000, We gave an algebro-geometric construction of the moduli spaces of stable parabolic connections over curves with unramified singularities, and showed the fundamental property of the Riemann-Hilbert correspondences. These results showed the geometric Painleve property of the nonlinear isomonodromic differential equations and established the geometry of isomonodromic deformations of connections, which enables us to investigate the phase space of differential equations deeply such as Okamoto's space of initial conditions for classical Painleve equations. Together with the progress in the field of higher dimensional birational geometry and the geometry related to mirror symmetry, these results reveal deep relations between algebraic geometry and integrable systems., kaken

Grant-in-Aid for Scientific Research (B), 2006, 2009, 18340010, Studies on moduli of stable sheaves, YOSHIOKA Kota; SAITO Masahiko; YAMADA Yasuhiko; NOUMI Masatoshi; NAKAJIMA Hiraku; MASTUSHITA Daisuke; INABA Michiaki, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Kobe University, 17110000, 13900000, 3210000, We derived the wall crossing formula and the blow-up formula of the Donaldson invariants. We also formulated K-theoretic analogue of the Doinaldson invariants and got the wall crossing formula. We studied the betation of the Fourier-Mukai transform and the stability condition ang got a nice result. As an application, we also studied the moduli of stable sheaves on abelian surfaces., kaken

Grant-in-Aid for Scientific Research (C), 2006, 2008, 18540034, Research on derived categories in algebraic geometry, ISHII Akira; TSUCHIMOTO Yoshifumi; INABA Michiaki; UEHARA Hokuto; SHIMADA Ichiro; SHUN-ICHI Kimura, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Hiroshima University, 4060000, 3400000, 660000, A型クライン特異点の極小解消上の例外集合に台を持つ連接層の導来圏に関して, Bridgelandの定義した安定性条件の空間を決定し, 特にそれが連結かつ単連結であることを示した. また, ダイマー模型にそれぞれ適当な条件を課すと, 付随する箙の表現のモジュライ空間が, 対応する3次元特異点のクレパント解消になり, 箙の道代数はその非可換クレパント解消であることを示した. 特殊McKay対応との関係も明らかにした., kaken

Grant-in-Aid for Scientific Research (B), 2005, 2008, 17340009, An research of algebraic K-theory of arithmetic varieti, TAKEDA Yuichiro; YUICHIRO Taguchi; EIICHI Sato; MICHIAKI Inaba; ASAKURA Masanori; NAKASHIMA Tohru, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Kyushu University, 6090000, 5400000, 690000, 本研究の目的は、キューブや代数サイクルといった幾何的な対象を用いて、代数的K理論の元を構成する方法を確立することであった。得られた結果は次のとおりである。(1)楕円曲面上の一次や二次のキューブで、そのBott-Chern形式がKronecker-Eisenstein級数を用いて表されるものを構成した。(2)Goncharovにより定義された代数的サイクル上の積分が、レギュレーター写像に一致することの証明を考案した。(3)Goncharovによる代数的サイクル上の積分をBlochのポリログサイクルに対して計算して、それがポリログ関数を用いて表わされることを示した。, kaken

若手研究(B), 2006, 2007, 18740011, 導来圏のモジュライ問題と可積分系の幾何学, 稲場 道明, 日本学術振興会, 科学研究費助成事業, 京都大学, 2000000, 2000000, 射影直線上の4点で確定特異点を持つ階数2の放物接続のモジュライ空間が、丁度パンルベ第6方程式の岡本初期値空間と一致するという結果を数年前に出した。これの証明は、直接的に示すのは困難であるため、一旦モジュライ空間のコンパクト化をして、放物φ接続のモジュライ空間というものを考え、これがパンルベ6型の岡本・パンルベ対と同型であることを示した。本年度はこれを非正則特異点を持つ放物接続の場合に考えようと試みた。実際考えたのは、射影直線上の3点で確定特異点を持ち、1点で非正則特異点を持つ放物接続のモジュライ空間についてであるが、この場合も、モジュライ空間をコンパクト化して岡本・パンルベ対との同型を与えるのが筋の良い方法と思われた。実際射影直線上の3点で確定特異点を持ち、1点で非正則特異点を持つ放物φ接続のモジュライ空間から2次のヒルゼブルフ曲面への射が構成できることまではわかった。しかし、この放物φ接続のモジュライ空間はどうやら特異点を持つようであり、パンルペ5型方程式の初期値空間のコンパクト化である岡本・パンルベ対との同型を作ることは不可能なようである。, kaken

Grant-in-Aid for Scientific Research (B), 2004, 2007, 16340049, Geometry and global analysis of Pailneve equations, IWASAKI Katsunori; KAJIWARA Kenji; KAMIMOTO Joe; SAITO Masa-hiko; INABA Mchiaki; HARAOKA Yoshishige, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Kyushu University, 9030000, 8400000, 630000, Many results have been obtained for Painleve equations, especially for Painleve VI equation and its generalization, Gamier systems, from the viewpoint of algebraic geometry and dynamical system theory. They consist of the establishments of laws of Painleve dynamics mainly based on algebraic geometry, and the elucidations of the global phenomena of Painleve dynamics mainly based on dynamical system theory. More explicitly, the results on the laws of Painleve dynamics include the construction of the phase spaces of Painleve dynamics as the moduli space of stable parabolic connections, the establishment of Riemann-Hilbert correspondence, a characterization of Backlund transformations in terms of the Riemann-Hilbert correspondence, the discovery of an initimate relation between Riccati solutions and singularity theory, an intrinsic introduction of the Hamiltonian structure of Painleve equations, and so on. On the other hand, among the results on the phenomena of Painleve dynamics, it is most remarkable that we were able to show that the nonlinear monodromy of the Painleve flow is chaotic along almost all loops in the space of time variable. Namely, the proof of the positivity of the topological entropy, the construction of a maximal-entropy hyperbolic invariant probability measure of saddle type, the establishment of an algorithm of calculating entropy in terms of the reduced word of a given loop and the geometric representation of a universal Coxeter group. These results clearly show that the Painleve equation is in fact a chaotic dynamical system, although it has previously been studied from the viewpoint of integrable systems only. So it is expected that our results would stimulate people to change minds in the future direction of research in the field of Painleve equations. The above-mentioned achievements are the results of many cooperative researches, attendances at various conferences and exchanges of ideas, making the best use of this grant. By virtue of this grant, we were also able to announce or describe the details of our results in various conferences, workshops and other academic meetings, either domestic or overseas. The international conferences on Painleve equations in which the head investigator were invited to give a lecture include Theories asymptotiques et equations de Painleve, Universite d'Angers, France; The Painleve equations and monodromy problems, Isaac Newton Institute, Cambridge University. In summary, the original aims of this project, i.e., to develop an algebraic geometry in order to lay a sound foundation of Painleve equations and to explore the global phenomena of Painleve dynamics, have largely been achieved. A further advances along the line of this project can be expected based on these achievements., kaken

連接層の導来圏のモジュライ構造の研究, 0, 0, 0, Competitive research funding

Study on the moduli structure of the derived category of choerent sheaves, 0, 0, 0, Competitive research funding