Chamber Structure and Wallcrossing in The ADHM Theory of Curves I
arXiv:0904.4451 · doi:10.1016/j.geomphys.2011.09.012
Abstract
ADHM invariants are equivariant virtual invariants of moduli spaces of twisted cyclic representations of the ADHM quiver in the abelian category of coherent sheaves of a smooth complex projective curve X. The goal of the present paper is to present a generalization of this construction employing a more general stability condition which depends on a real parameter. This yields a chamber structure in the ADHM theory of curves, residual ADHM invariants being defined by equivariant virtual integration in each chamber. Wallcrossing results and applications to local stable pair invariants will be presented in the second part of this work.
51 pages, AMS Latex, version 2: partial rewriting, relation to prior existing work clarified, references added and some errors corrected; wallcrossing result generalized and moved to second part; version 3: some redundant lemmas removed; v4: 35 pages, many proofs simplified, results unchanged; to appear in J. Geom. Phys
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Cited by in corpus (14)
- Towards a mathematical definition of Coulomb branches of -dimensional gauge theories, II
- Parabolic refined invariants and Macdonald polynomials
- Geometric engineering of (framed) BPS states
- Rank Two ADHM Invariants and Wallcrossing
- Wallcrossing and Cohomology of The Moduli Space of Hitchin Pairs
- Chamber Structure and Wallcrossing in the ADHM Theory of Curves II
- Wall-crossing formulas for framed objects
- HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants
- Stable quasimaps to holomorphic symplectic quotients
- BPS states and the P=W conjecture
- Homology of twisted quiver bundles with relations
- D0-D6 states counting and GW invariants
- On Some Computations of Higher Rank Refined Donaldson-Thomas Invariants
- Wall-crossings for Twisted Quiver Bundles