Daisuke Matsushita (Faculty of Science　Mathematics　Mathematics) | Researcher Directory

Researcher Database

Daisuke Matsushita

Faculty of Science　Mathematics　Mathematics

Associate Professor

Last Updated :2021/01/22

- 1997 The University of Tokyo Graduate School, Division of Mathematical Sciences

- 1994 The University of Tokyo Graduate School, Division of Mathematical Sciences

On deformations of Lagrangian fibrations
MATSUSHITA Daisuke
K3 surfaces and their moduli, Progr. Math., Birkhäuser/Springer 315 237 - 243 2016 [Refereed][Not invited]

On base manifolds of Lagrangian fibrations
Matsushita Daisuke
SCIENCE 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.

On almost holomorphic Lagrangian fibrations
Daisuke Matsushita
MATHEMATISCHE 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.

On nef reductions of projective irreducible symplectic manifolds
Daisuke Matsushita
MATHEMATISCHE 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.

Higher direct images of dualizing sheaves of Lagrangian fibrations
D Matsushita
AMERICAN 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.

Holomorphic symplectic manifolds and Lagrangian fibrations
D Matsushtia
ACTA 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.

Simultaneous minimal models of homogeneous toric deformations
Daisuke Matsushita
Kodai 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.

On singular fibres of Lagrangian fibrations over holomorphic symplectic manifolds
D Matsushita
MATHEMATISCHE 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.

Addendum: "On fibre space structures of a projective irreducible symplectic manifold"
Topology 40 (2) 431 - 432 2001 [Refereed][Not invited]

Equidimensionality of Lagrangian fibrations on holomorphic symplectic manifolds
D Matsushita
MATHEMATICAL 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.

On fibre space structures of a projective irreducible symplectic manifold
D Matsushita
TOPOLOGY 38 (1) 79 - 83 0040-9383 1999/01 [Not 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.

On a relation among toric minimal models
D Matsushita
PROCEEDINGS 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 flops
Saitama Mathematical Journal 15 47 - 54 1997 [Refereed][Not invited]

Effective base point freeness
Daisuke Matsushita
Kodai 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.