Supersymmetric D-branes supported on the complex two-dimensional base S of the local
Calabi–Yau threefold KS are described by semi-stable coherent sheaves on S. Under …

We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in
any triangulated category D with arbitrary (set-indexed) coproducts. We show that …

We study the birational properties of geometrically rational surfaces from a derived
categorical perspective. In particular, we give a criterion for the rationality of a del Pezzo …

Derived categories of singular surfaces Page 1 © 2021 European Mathematical Society
Published by EMS Press. This work is licensed under a CC BY 4.0 licence. J. Eur. Math. Soc. 24 …

Non-commutative crepant resolutions are algebraic objects defined by Van den Bergh to
realize an equivalence of derived categories in birational geometry. They are motivated by …

We work out properties of smooth projective varieties X over a (not necessarily algebraically
closed) field k that admit collections of objects in the bounded derived category of coherent …

In this paper, we construct infinitely many examples of toric Fano varieties with Picard
number three, which do not admit full exceptional collections of line bundles. In particular …

Hochschild Dimensions of Tilting Objects Page 1 M. Ballard and D. Favero (2012) “Hochschild
Dimensions of Tilting Objects,” International Mathematics Research Notices, Vol. 2012, No. 11 …

Let X be any rational surface. We construct a tilting bundle T on X. Moreover, we can choose
T in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded …

Our main goal is to give a sense of recent developments in the (stable) rationality problem
from the point of view of unramified cohomology and 0-cycles as well as derived categories …