Chamber Structure and Wallcrossing in the ADHM Theory of Curves II
Wu-yen Chuang, Duiliu-Emanuel Diaconescu, Guang Pan
TL;DR
This paper investigates the wallcrossing phenomena in ADHM invariants of curves, deriving formulas using advanced algebraic and enumerative theories, and applies these results to various problems in algebraic geometry and string theory.
Contribution
It develops new wallcrossing formulas for ADHM invariants of curves using stack function Ringel-Hall algebras and generalized Donaldson-Thomas invariants, extending previous work.
Findings
Derived explicit wallcrossing formulas for ADHM invariants
Established strong rationality for local stable pair invariants of higher genus curves
Compared new formulas with existing wallcrossing formulas of Kontsevich-Soibelman and halo formulas of Denef-Moore
Abstract
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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