Chamber Structure and Wallcrossing in the ADHM Theory of Curves II

Details Chamber Structure and Wallcrossing in the ADHM Theory of Curves II Chamber Structure and Wallcrossing in the ADHM Theory of Curves II

2009-08-07

arxiv.org/abs/0908.1119v4

J. Geom. Phys. 62 (2012) 548

Mathematics

Algebraic Geometry

32 pages, AMS LaTex; v.2: Thm 1.2 improved; v3: many proofs simplified based on a remark of Dominic Joyce, results unchanged;

Scientific paper

This is the second part of a project concerning variation of stability and chamber structure for ADHM invariants of curves. Wallcrossing formulas for such invariants are derived using the theory of stack function Ringel-Hall algebras constructed by Joyce and the theory of generalized Donaldson-Thomas invariants of Joyce and Song. Some applications are presented, including strong rationality for local stable pair invariants of higher genus curves and comparison with wallcrossing formulas of Kontsevich and Soibelman, and the halo formula of Denef and Moore.

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