Moduli spaces of stable pairs

Yinbang Lin

Vol. 294 (2018), No. 1, 123–158

DOI: 10.2140/pjm.2018.294.123

Abstract

We construct a moduli space of stable pairs over a smooth projective variety, parametrizing morphisms from a fixed coherent sheaf to a varying sheaf of fixed topological type, subject to a stability condition. This generalizes the notion used by Pandharipande and Thomas, following Le Potier, where the fixed sheaf is the structure sheaf of the variety. We then describe the relevant deformation and obstruction theories. We also show the existence of the virtual fundamental class in special cases.

Keywords

moduli space, stable pair, deformation, obstruction, virtual fundamental class

Mathematical Subject Classification 2010

Primary: 14D20

Secondary: 14J60, 14N35

Milestones

Received: 3 June 2016

Revised: 28 August 2017

Accepted: 31 October 2017

Published: 5 January 2018