Mathematical Research Letters

Volume 30 (2023)

Number 4

Moduli spaces of semistable pairs on projective Deligne–Mumford stacks

Pages: 1131 – 1205

DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n4.a7

Author

Yijie Lin (School of Mathematics, Sun Yat-Sen University, Zhuhai, China; and School of Mathematics and Statistics, Fujian Normal University, Fuzhou, China)

Abstract

We generalize the construction of a moduli space of semistable pairs parametrizing isomorphism classes of morphisms from a fixed coherent sheaf to any sheaf with fixed Hilbert polynomial under a notion of stability to the case of projective Deligne–Mumford stacks.We study the deformation and obstruction theories of stable pairs, and then prove the existence of virtual fundamental classes for some cases of dimension two and three. This leads to a definition of Pandharipande–Thomas invariants on three-dimensional smooth projective Deligne–Mumford stacks.

Full Text (PDF format)

The author was partially supported by the Chinese Universities Scientific Fund (74120-31610010), and by the Guangdong Basic and Applied Basic Research Foundation (2019A1515110255).

Received 30 September 2020

Received revised 6 May 2021

Accepted 26 July 2022

Published 3 April 2024