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Kawamata Yujiro | Kawamata Takayuki | Kawamata T. | Kawamata Ryota | Kawamata R. | Kawamata I. | Kawamata Masahiro

16 Jun 2020
math.AG
arxiv.org/abs/2006.09547

We consider non-commutative deformations of sheaves on algebraic varieties. We develop some tools to determine parameter algebras of versal non-commutative deformations for partial simple collections and the structure sheaves of smooth rational curves. We apply them to universal flopping contractions of length 2 and higher. We confirm Donovan-Wemyss conjecture in the case of deformations of Laufer's flops.

29 Aug 2019
math.AG
arxiv.org/abs/1908.11483

We review the theory of non-commutative deformations of sheaves and describe a versal deformation by using an A-infinity algebra and the change of differentials of an injective resolution. We give some explicit non-trivial examples.

02 Mar 2019
math.AG
arxiv.org/abs/1903.00801

We consider semi-orthogonal decompositions of derived categories for 3-dimensional projective varieties in the case when the varieties have ordinary double points.

13 Jun 2018
math.AG
arxiv.org/abs/1806.04858

We determine versal non-commutative deformations of some simple collections in the categories of perverse coherent sheaves arising from tilting generators for projective morphisms.

19 Oct 2017
math.AG
arxiv.org/abs/1710.07370

This paper is based on a talk at a conference "JDG 2017: Conference on Geometry and Topology". We survey recent progress on the DK hypothesis connecting the birational geometry and the derived categories stating that the K-equivalence of smooth projective varieties should correspond to the equivalence of their derived categories, and the K-inequality to the fully faithful embedding.

23 Sep 2017
math.AG
arxiv.org/abs/1709.08065

We generalize a result of Fujita, on the decomposition of Hodge bundles over curves, to the case of a higher dimensional base.

29 Sep 2016
math.AG
arxiv.org/abs/1609.09540

We prove that the equivariant derived category for a finite subgroup of GL(3,C) has a semi-orthogonal decomposition into the derived category of a certain partial resolution, called a maximal Q-factorial terminalization, of the corresponding quotient singularity and a relative exceptional collection. This is a generalization of a result of Bridgeland, King and Reid.

18 Dec 2015
math.AG
arxiv.org/abs/1512.06170

We shall develop a theory of multi-pointed non-commutative deformations of a simple collection in an abelian category, and construct relative exceptional objects and relative spherical objects in some cases. This is inspired by a work by Donovan and Wemyss.

27 Dec 2014
math.AG
arxiv.org/abs/1412.8040

We prove derived McKay correspondence in special cases and the decomposition of toric K-equivalence into flops.

13 Feb 2012
math.AG math.AC
arxiv.org/abs/1202.2696

We prove that a Mori dream space over a field of characteristic zero is of Calabi-Yau type if and only if its Cox ring has at worst log canonical singularities. By slightly modifying the arguments we also reprove the characterization of the varieties of Fano type by the log terminality of the Cox rings.