Researcher Database
Last Updated :2024/07/25
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Profile and Settings
Affiliation
- Hokkaido University, Faculty of Science, Department of Mathematics, Mathematics, Associate Professor
Profile and Settings
Name (Japanese)
MatsushitaName (Kana)
DaisukeName
200901083009240684
Alternate Names
Affiliation
- Hokkaido University, Faculty of Science, Department of Mathematics, Mathematics, Associate Professor
Achievement
Research Interests
Research Areas
Education
- - 1997 The University of Tokyo
- - 1997 The University of Tokyo Graduate School, Division of Mathematical Sciences
- - 1994 The University of Tokyo
- - 1994 The University of Tokyo Graduate School, Division of Mathematical Sciences
- - 1992 The University of Tokyo Faculty of Science Department of Mathematics
- - 1992 The University of Tokyo Faculty of Science
Published Papers
- On isotropic divisors on irreducible symplectic manifoldsDaisuke MstsushitaHigher dimensional algebraic geometry—in honour of Professor Yujiro Kawamata's sixtieth birthday 74 291 - 312 2017 [Refereed]
- Daisuke MatsushitaProgress in Mathematics 315 237 - 243 2296-505X 2016 [Refereed][Not invited]
Let X be an irreducible symplectic manifold and Def(X) be the Kuranishi family. Assume that X admits a Lagrangian fibration. We prove that X can be deformed preserving a Lagrangian fibration. More precisely, there exists a smooth hypersurface H of Def(X), such that the restriction family χ ×Def(X) H admits a family of Lagrangian fibrations over H. - Matsushita DaisukeSCIENCE CHINA-MATHEMATICS 58 (3) 531 - 542 1674-7283 2015/03 [Refereed][Not invited]
We consider base spaces of Lagrangian fibrations from singular symplectic varieties. After defining cohomologically irreducible symplectic varieties, we construct an example of Lagrangian fibration whose base space is isomorphic to a quotient of the projective space. We also prove that the base space of Lagrangian fibration from a cohomologically symplectic variety is isomorphic to the projective space provided that the base space is smooth. - Daisuke MatsushitaMATHEMATISCHE ANNALEN 358 (3-4) 565 - 572 0025-5831 2014/04 [Refereed][Not invited]
We prove that the pull back of an ample line bundle by an almost holomorphic Lagrangian fibration is nef. As an application, we show birational semi rigidity of Lagrangian fibrations. - Daisuke MatsushitaMATHEMATISCHE ZEITSCHRIFT 258 (2) 267 - 270 0025-5874 2008/02 [Refereed][Not invited]
Let X be a projective irreducible symplectic manifold and L be a non trivial nef divisor on X. Assume that the nef dimension of L is strictly less than the dimension of X. We prove that L is semiample. - Daisuke MatsushitaAMERICAN JOURNAL OF MATHEMATICS 127 (2) 243 - 259 0002-9327 2005/04 [Refereed][Not invited]
Let f : X -> S be a Lagrangian fibration between projective varieties. We prove that R-f(i)*O-X congruent to Omega(S)(i) if S is smooth. Suppose that X is an irreducible symplectic manifold or a certain moduli space of semistable torsion free sheaves on a K3 surface, the Hodge numbers satisfy h(p,q)(S) = h(p,q)(P-n), where n = dimS. If S congruent to P-n and X is an irreducible symplectic manifold, there exists a hypersurface M-f of the Kuranishi space of X such that every member of the Kuranishi family over Mf admits a Lagrangian fibration over P-n. - Daisuke MatsushtiaACTA APPLICANDAE MATHEMATICAE 75 (1-3) 117 - 123 0167-8019 2003/01 [Refereed][Not invited]
We introduce the geometrical nature of fibre space structures of an irreducible symplectic manifold and holomorphic Lagrangian fibrations. - Daisuke MatsushitaKodai Mathematical Journal 25 (1) 54 - 60 0386-5991 2002 [Refereed][Not invited]
Every flat family of Du Val singularities admits a simultaneous minimal resolution after a finite base change. We investigate a flat family of isolated Gorenstein toric singularities and prove that there exists a simultaneous partial resolution. © 2002, Department of Mathematics, Tokyo Institute of Technology. All rights reserved. - Daisuke MatsushitaMATHEMATISCHE ANNALEN 321 (4) 755 - 773 0025-5831 2001/12 [Refereed][Not invited]
We classify singular fibres over general points of the discriminant locus of projective Lagrangian fibrations over 4-dimensional holomorphic symplectic manifolds. The singular fibre F is the following either one: F is isomorphic to the product of an elliptic curve and a Kodaira singular fibre up to finite unramified covering or F is a normal crossing variety consisting of several copies of a minimal elliptic ruled surface of which the dual graph is Dynkin diagram of type A(n), (A) over tilde (n) or (D) over tilde (n). Moreover, we show all types of the above singular fibres actually occur. - Daisuke MatsushitaTOPOLOGY 40 (2) 431 - 432 0040-9383 2001/03 [Refereed][Not invited]
- Daisuke MatsushitaMATHEMATICAL RESEARCH LETTERS 7 (4) 389 - 391 1073-2780 2000/07 [Refereed][Not invited]
We prove that every irreducible component of every fibre of Lagrangian fibrations on holomorphic symplectic manifolds is a Lagrangian subvariety. Especially, Lagrangian fibrations are equidimensional. - Daisuke MatsushitaTOPOLOGY 38 (1) 79 - 83 0040-9383 1999/01 [Refereed][Not invited]
In this note, we investigate fibre space structures of a projective irreducible symplectic manifold. We prove that a 2n-dimensional projective irreducible symplectic manifold admits only an n-dimensional fibration over a Fano variety which has only Q-factorial log-terminal singularities and whose Picard number is one, Moreover we prove that a general fibre is an abelian variety up to finite unramified cover, especially, for 4-fold, a general fibre is an abelian surface and all fibres are equidimensional. (C) 1998 Elsevier Science Ltd. All rights reserved. - Daisuke MatsushitaPROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 73 (6) 100 - 102 0386-2194 1997/06 [Refereed][Not invited]
Every normal surface singularity has a unique minimal resolution. On the contrary, a minimal terminalization of higher dimensional singularity is not unique. In this note, we prove that there exists a correspondence between minimal terminalizations of a toric canonical singularity and radicals of initial ideals of term order represented by weight vector. - On smooth 4-fold flopsDaisuke MatsushitaSaitama Mathematical Journal 15 47 - 54 1997 [Refereed][Not invited]
- Daisuke MatsushitaKodai Mathematical Journal 19 (1) 87 - 116 0386-5991 1996 [Refereed][Not invited]
It is an interesting problem to know when the adjoint bundle Kx+mL is free or very ample. Recently Ein-Lazarsfeld states very explicit numerical conditions about L such that Kx+L becomes free on a smooth 3-fold. In this paper, the author wants to enlarge their results on a singular 3-fold. © 1996, Department of Mathematics, Tokyo Institute of Technology. All rights reserved.
Association Memberships
Research Projects
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2024/04 -2029/03Author : 小野 薫, 入江 慶, 枡田 幹也, 三松 佳彦, 赤穂 まなぶ, 秦泉寺 雅夫, 大場 貴裕, 吉安 徹, 松下 大介
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2021/04 -2026/03Author : 並河 良典, 望月 拓郎, 吉川 謙一, 尾高 悠志, 吉岡 康太, 森脇 淳, 疋田 辰之, 松下 大介
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2019/04 -2024/03Author : 小野 薫, 石川 剛郎, 枡田 幹也, 三松 佳彦, 赤穂 まなぶ, 入江 慶, 秦泉寺 雅夫, 松下 大介, 石川 卓, 泉屋 周一倉西構造による仮想的基本類・基本鎖の理論の一般論をまとめ、2020 年に書籍として出版した。擬正則曲線の moduli 空間や、それを用いた代数構造の構成をこの一般論の枠組みで実現することについては、以下の成果がある。moduli 空間の倉西構造の滑らかさを示した論文も出版決定となった。それを基礎にして、周期的ハミルトン系の場合の linear K-system の構成、周期的ハミルトン系の Floer (co)homology の新しい方法を論文にまとめた。Lagrange 部分多様体に付随する tree-like K system の構成などについての論文を投稿に向けて再点検した。(以上は、深谷氏、Oh 氏、太田氏との共同研究である) symplectic orbifold の Lagrangian に対する Floer 理論については、clean intersection となる Lagrangians の対の twisted sector の概念を得た。それを用いてLagrangian intersection の Floer 理論の枠組みができる。(Chen 氏、Wang 氏との共同研究) また、研究員として吉安徹氏を雇用し、h-原理 特に loose Legendre 部分多様体などについての継続的議論を通してシンプレクティック構造、接触構造の柔な側面について理解を深めた。
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2018/04 -2023/03Author : 松下 大介いわゆる Galois 理論とは体 k の有限次拡大体 K があった時, K と k の間の部分体 H の集合と K の k を固定する自己同型群 Gal(K/k) の部分群 G の集合の間に対応がある, という理論を指す. この対応を代数多様体の定義体と有理関数体に対して以下のように拡張することを試みている.
作業仮説 : k 上定義された代数多様体 X に対し, X の自己同型群を Aut(X) とする. X の有理関数体 k(X) の k 上超越次数が 1 以上で k(X) よりも超越次数が小さい部分体と Aut(X) の almost abelian という可換な群に極めて近い性質を持つ無限位数の部分群の間に対応がある.
2021 年度は上記の仮説を X が既約シンプレクティック多様体である時, SYZ 予想と呼ばれる予想が正しい ( これは 2021 年度知られている既約シンプレクティック多様体の全ての具体例で成立することが既に示されている ) と仮定した時に考察し, Aut(X) の almost abelian な無限位数の部分群の k(X) の固定体の超越次数は必ず X の次元の半分となり, 逆に k(X) の超越次数が 1 より大きい部分体 H に対して, Aut(X) の H を固定する部分群は almost abelian となることを示した また SYZ 予想を仮定しない証明を見出す準備として twisted homogeneous coordinate ring と呼ばれる対象について調べた. これは X の自己同型に応じて定まる非可換な字数付き環で, その交換子イデアルが自己同型の固定点集合の定義イデアルとなる, ということを示した. - Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2014/04 -2019/03Author : ONO Kaoru, Ogawa NoboruFloer theory and the theory of pseudo-holomorphic curves have provided powerful tools in the study of symplectic geometry and brought many important results. During the academic years 2014-2018, the following achievements on Floer theory and its applications were made public:Lagrangian Floer theory and mirror symmetry on compact toric manifolds (joint paper, Asterisque 376, 2016), Anti-symplectic involution and Floer cohomology (joint paper, Geometry and Topology, 2016).
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2014/04 -2018/03Author : MATSUSHITA DaisukeWe investigated the linear system associated to ample divisors and an automorphism group of an irreducible symplectic manifold using deformation of complex structure. Regarding the former, we obtain the following result. Let X be the set of the complex structures which defining the mapping and Y the set of the complex structures which defining the embedding in the projective space. Both X and Y are open in the space of deformation of the complex structures of irreducible symplectic manifolds. With respect to the latter, by appropriately deforming the complex structure, we prove that an automorphism group of irreducible symplectic manifold contain an infinite cyclic group whose rank equals to the second Betti number minus two.
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2012/05 -2017/03Author : 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 TaroWe 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.
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2009/04 -2014/03Author : ONO Kaoru, IZUMIYA Shyuichi, JINZENJI Masao, MATSUSHITA Daisuke, ISHIKAWA Goo, YAMAGUCHI Keizo, TAKAKURA TatsuruSymplectic structure is a geometric structure, which appeared in the understanding of Hamilton's equation of motion. In recent years, there has been profound development in the geometric study of symplectic structures. In particular, combined with the mathematical study on mirror symmetry, symplectic geometry attracts attentions from many researchers. The investigator has been working on Floer theory, which plays a significant role in symplectic geometry, and its applications. In this research project, we studied Floer theory for Lagrangian torus fibers in toric manifold in a concrete way and obtained various interesting results.
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2011 -2012Author : MATSUSHITA Daisuke, FUJINO Osamu, KAWAKITA Masayuki, TAKAGI HiromichiLet us consider a smooth abelian fibration over a punctured disk or an open set of polydisk which obtained by removing a hypersurface. It is natural question whether these families can be extended over a disk or a polydisk. On 80th, it was announced that we could obtain such a relative compactification with a incomplete proof. Since semidarkness of the proof, there are several results with technical assumptions. By this result, we may get rid of these assumptions and obtain idealistic results.
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2009 -2012Author : MATSUSHITA DaisukeWe show that the base space of a Lagrangian fibration is a projective space if the source symplectic variety satisfies certain numerical conditions. We obtain the necessary and sufficient condition of existence of a Lagrangian fibration for all known examples. We also show smoothness of components of the relative moduli space of aLagrangian fibration which parametrize invertible sheaves on each fibre.
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2007 -2011Author : 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 YukinobuWe 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.
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2006 -2009Author : YOSHIOKA Kota, SAITO Masahiko, YAMADA Yasuhiko, NOUMI Masatoshi, NAKAJIMA Hiraku, MASTUSHITA Daisuke, INABA MichiakiWe 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.
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2006 -2008Author : MATSUSHITA Daisukeシンプレクティック多様体に入るラグランジアンファイブレーションについて, 特異ファイバーの構造を決定した。またラグランジアンファイブレーションを保ったまま変形出来るシンプレクティック多様体がそのモジュライ空間の中で余次元1の族をなすことを示した。さらにシンプレクティック多様体の双有理的な特質の一つを見出した。
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2006 -2008Author : KAORU Ono, KEIZO Yamaguchi, SHYUICHI Izumiya, GOO Ishikawa, MASAO Jinzenji, DAISUKE Matsushita, KENJI Fukaya, HIROSHI OhtaLagrange部分多様体のFloer理論の枠組みおよび基礎付けを深谷氏、Oh氏、太田氏との共同研究で行った。Lagrange部分多様体のFloer理論のシンプレクティック幾何学へのいくつかの応用も得た。また、トーリック多様体のLagrangeトーラスファイバーのFloer理論にも着手し、Hamilton displaceablityやdisplacement energyについての結果を得た。
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2001 -2004Author : YOSHIDA Tomoyuki, YAMASHITA Hiroshi, MATSUSHITA Daisuke, TAKEGAHARA Yugen, YAMADA Hirohumi, YAMAKI Hiroyoshi1.Asai-Yoshida's conjecture on the number of group homomorphisms has a connection with p-adic anallysis (Yoshida, Takegahara, K.Conrad, etc.). Furthermore, Yoshida solved the conjecture for the homomorphisms from the fundamental group of a compact Riemann surface whose importence in quantum field theory was pointed by M.Mulase. 2.Yoshida and Oda accomplished a fundamental theory of crossed Burnside rings of finite groups. 3.Yoshida, Sasaki, Oda study cohomology theory of finite groups, especially Hochschild cohomology, crossed Mackey functors and quantum doubles of group algebra. 4.Yoshida, Bannai and Keisuke Shiromoto sutudies combinatorics, in particular, distance regular graphs, designs and code theory, especially an application of homological algebra to the theory of codes on a ring. 5.Koshitani studies modular representation thoery of finite groups and gave an affirmative answer to the Broue conjecture for groups with some special defect groups. 6.Nakamura and Yamashita studied some related areas (algebraic geometry and representation theory) and gave some interested results, especially a relation with finite simple groups. 7.We invited three mathematicians from abroad. ・2001 FAN Yun(Wuhan U.) Talk on Broue conjecture(Kyushu Univ.) ・2003 Keith CONRAD(Connecticut U.) Talk of p-adic analysis, number theory(Hokkaido U., Kyoto U.) ・2004 Segre BOUC(CNRS) Talk on Dade groups and Burnside rings (Hokaido U., Kyoto U.) A large number of results of this research has been printed and published. The remainder results will be serially published. The investigator gave some talks related to this research in some conferences-- "Generating functions and related topics" (Sapporo 2001), "20-th Symposium on Algebraic Combinatorics (Kyoto 2002), "Extended Group Seminar" (Sapporo 2002,2004, and so on.
- 正則シンプレクティック多様体Date (from‐to) : 1997
- Holomorphic symplectic manifoldDate (from‐to) : 1997