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Izv. RAN. Ser. Mat., 2019, Volume 83, Issue 4, Pages 50–85 (Mi izv8830)  

Equivariant exceptional collections on smooth toric stacks

L. A. Borisova, D. O. Orlovb

a 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.

Funding Agency Grant Number
National Science Foundation DMS-1601907
L. A. Borisov was partially supported by NSF grant DMS-1601907.


DOI: https://doi.org/10.4213/im8830

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

Bibliographic databases:

UDC: 512.7
MSC: Primary 14F05; Secondary 14M25, 55U10
Received: 21.06.2018

Citation: L. A. Borisov, D. O. Orlov, “Equivariant exceptional collections on smooth toric stacks”, Izv. RAN. Ser. Mat., 83:4 (2019), 50–85; Izv. Math., 83:4 (2019), 698–730

Citation in format AMSBIB
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  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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