Asian Journal of Mathematics

Volume 25 (2021)

Number 4

On strong exceptional collections of line bundles of maximal length on fano toric Deligne–Mumford stacks

Pages: 505 – 520

DOI: https://dx.doi.org/10.4310/AJM.2021.v25.n4.a3

Authors

Lev Borisov (Department of Mathematics, Rutgers University, Piscataway, New Jersey, U.S.A.)

Chengxi Wang (Department of Mathematics, Rutgers University, Piscataway, New Jersey, U.S.A.)

Abstract

We study strong exceptional collections of line bundles on Fano toric Deligne–Mumford stacks $\mathbb{P}_\Sigma$ with rank of Picard group at most two. We prove that any strong exceptional collection of line bundles generates the derived category of $\mathbb{P}_\Sigma$, as long as the number of elements in the collection equals the rank of the (Grothendieck) $K$‑theory group of $\mathbb{P}_\Sigma$.

Keywords

toric Deligne–Mumford stacks, Picard groups, strong exceptional collections, line bundles, derived categories

2010 Mathematics Subject Classification

Primary 14M25. Secondary 14C20, 14F05.

Full Text (PDF format)

Received 21 September 2020

Accepted 10 December 2020

Published 25 April 2022