15 citations · 32 across the 13 of their papers we have counts for
13 papers
Stability conditions and infinitesimal deformation of curves
Kotaro Kawatani
Let be an infinitesimal deformation of a smooth projective curve over a field. We study stability conditions under such deformations and show that the derived pu…
-linear triangulated categories and stability conditions
Kotaro Kawatani
Let be a commutative ring. We introduce the notion of support of objects in an -linear triangulated category. As an application, we study the non-existence of Bridgeland sta…
On a deformation of gluing stability conditions
Kotaro Kawatani
On a triangulated category equipped with a semiorthogonal decomposition , Collins and Polishchuk develop a glui…
Stability conditions on affine Noetherian schemes
Kotaro Kawatani
We show that the existence of locally finite stability conditions on the bounded derived category of coherent sheaves on an affine Noetherian scheme is equi…
Stability conditions on morphisms in a category
Kotaro Kawatani
Let be the homotopy category of a stable infinity category . Then the homotopy category of morphisms in the sta…
Pure sheaves and Kleinian singularities
Kotaro Kawatani
Grothendieck proved that any locally free sheaf on a projective line over a field (uniquely) decomposes into a direct sum of line bundles. Ishii and Uehara construct an analogue of…
Nonexistence of semiorthogonal decompositions and sections of the canonical bundle
Kotaro Kawatani, Shinnosuke Okawa
For any admissible subcategory of the bounded derived category of coherent sheaves on a smooth proper variety, we prove that sections of the canonical bundle impose a strong constr…
Fourier-Mukai transformations on K3 surfaces with and Atkin-Lehner involutions
Kotaro Kawatani
We show that there is a surjection from the Fourier-Mukai transformations on projective K3 surfaces with the Picard number to so called to the group of Atkin-Lehner involu…
A hyperbolic metric and stability conditions on K3 surfaces with ρ=1
Kotaro Kawatani
In this article we introduce a hyperbolic metric on the (normalized) space of stability conditions on projective K3 surfaces with Picard rank . And we show that all wa…
Stability of Gieseker stable sheaves on K3 surfaces in the sense of Bridgeland and some applications
Kotaro Kawatani
We show that some Gieseker stable sheaves on a projective K3 surface are stable with respect to a stability condition of Bridgeland on the derived category of if the stabil…
The group of autoequivalences and the Fourier-Mukai number of a projective manifold
Kotaro Kawatani
Let be a smooth projective variety and $\Aut (D(X))$ the group of autoequivalences of the derived category of . In this paper we show that has no Fourier-Mukai partner o…
Stability conditions and -stable sheaves on K3 surfaces with Picard number one
Kotaro Kawatani
In this article, we show that some semi-rigid -stable sheaves on a projective K3 surface with Picard number 1 are stable in the sense of Bridgeland's stability condition. As…
On the birational geometry for irreducible symplectic 4-folds related to the Fano schemes of lines
Kotaro Kawatani
There is two group actions on the Fano scheme of lines such that the quotient becomes an irreducible symplectic manifold. We showed that both quotients are birational to the genera…