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

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Non-commutative deformations of perverse coherent sheaves and rational curves

Kawamata Yujiro
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.

On non-commutative formal deformations of coherent sheaves on an algebraic variety

Kawamata Yujiro
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.

Semi-orthogonal decomposition of a derived category of a 3-fold with an ordinary double point

Kawamata Yujiro
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.

Non-commutative deformations of simple objects in a category of perverse coherent sheaves

Kawamata Yujiro
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.

Birational geometry and derived categories

Kawamata Yujiro
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.

Fujita decomposition over higher dimensional base

Catanese Fabrizio, Kawamata Yujiro
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.

Derived McKay correspondence for GL(3,C)

Kawamata Yujiro
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.

On multi-pointed non-commutative deformations and Calabi-Yau threefolds

Kawamata Yujiro
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.

Derived categories of toric varieties III

Kawamata Yujiro
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.

Mori dream spaces of Calabi-Yau type and the log canonicity of the Cox rings

Kawamata Yujiro, Okawa Shinnosuke
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.