Vol. 294, No. 1, 2018

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Moduli spaces of stable pairs

Yinbang Lin

Vol. 294 (2018), No. 1, 123–158

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.

moduli space, stable pair, deformation, obstruction, virtual fundamental class
Mathematical Subject Classification 2010
Primary: 14D20
Secondary: 14J60, 14N35
Received: 3 June 2016
Revised: 28 August 2017
Accepted: 31 October 2017
Published: 5 January 2018
Yinbang Lin
Department of Mathematics
Northeastern University
Boston, MA
United States
Yau Mathematical Sciences Center
Tsinghua University