This article is cited in 2 papers

Equivariant exceptional collections on smooth toric stacks

L. A. Borisov^a, D. O. Orlov<sup>b

a</sup> Department of Mathematics, Rutgers University, USA
^b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We study the bounded derived categories of torus-equivariant coherent sheaves on smooth toric varieties and Deligne–Mumford stacks. We construct and describe full exceptional collections in these categories. We also observe that these categories depend only on the $\mathrm{PL}$-homeomorphism type of the corresponding simplicial complex.

Keywords: toric varieties and stacks, equivariant coherent sheaves, derived categories, exceptional collections, simplicial complexes.

UDC: 512.7

MSC: Primary 14F05; Secondary 14M25, 55U10

Received: 21.06.2018

DOI: 10.4213/im8830

 English version: Izvestiya: Mathematics, 2019, 83:4, 698–730

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