Cobordism invariants of the moduli space of stable pairs

Abstract

For a quasi-projective scheme M which carries a perfect obstruction theory, we construct the virtual cobordism class of M. If M is projective, we prove that the corresponding Chern numbers of the virtual cobordism class are given by integrals of the Chern classes of the virtual tangent bundle. Further, we study cobordism invariants of the moduli space of stable pairs introduced by Pandharipande-Thomas. Rationality of the partition function is conjectured together with a functional equation, which can be regarded as a generalization of the rationality and 1/q <-> q symmetry of the Calabi-Yau case. We prove rationality for nonsingular projective toric 3-folds by the theory of descendents.

21 pages. Some typos fixed. To appear in J. London Math. Soc

References in corpus (5)

• Algebraic cobordism
• Gromov-Witten/Pairs descendent correspondence for toric 3-folds
• Derived algebraic cobordism
• Generating functions of stable pair invariants via wall-crossings in derived categories
• Descendents on local curves: Stationary theory

Cited by in corpus (8)

• Equivariant K-theory and refined Vafa-Witten invariants
• Virtual refinements of the Vafa-Witten formula
• Quot schemes of curves and surfaces: virtual classes, integrals, Euler characteristics
• The virtual K-theory of Quot schemes of surfaces
• A rank 2 Dijkgraaf-Moore-Verlinde-Verlinde formula
• The homology of moduli stacks of complexes
• Sheaves on surfaces and virtual invariants
• Wall-crossing for punctual Quot-schemes