Tilting generators via ample line bundles (2008)
Toda, Yukinobu, Uehara, Hokuto
It is known that a tilting generator on an algebraic variety $X$ gives a derived equivalence between $X$ and a certain non-commutative algebra. In this paper, we explain a method to construct a...
Three-dimensional terminal toric flips (2008)
Fujino, Osamu, Sato, Hiroshi, Takano, Yukishige, Uehara, Hokuto
We describe three-dimensional terminal toric flips. We obtain the complete local description of three-dimensional terminal toric flips.
Stability conditions on $A_n$-singularities (2006)
Ishii, Akira, Ueda, Kazushi, Uehara, Hokuto
We study the spaces of locally-finite stability conditions on the derived categories of coherent sheaves on the minimal resolutions of $A_n$-singularities supported at the exceptional sets. Our main...
In this article, we study the group of autoequivalences of derived categories of coherent sheaves on the minimal resolution of An-singularities on surfaces. Our main result is to find generators of...
In this article, we study the group of autoequivalences of derived categories of coherent sheaves on the minimal resolution of $A_n$-singularities on surfaces. Our main result is to find generators...
Calabi--Yau threefolds with infinitely many divisorial contractions (2003)
We study Calabi--Yau 3-folds with infinitely many divisorial contractions. We also suggest a method to describe Calabi--Yau 3-folds with the infinite automorphism group.
An example of Fourier--Mukai partners of minimal elliptic surfaces (2003)
Let $X$ and $Y$ be smooth projective varieties over $\C$. We say that $X$ and $Y$ are \emph{D-equivalent} (or, $X$ is a \emph{Fourier--Mukai partner} of $Y$) if their derived categories of bounded...