Chamber Structure and Wallcrossing in The ADHM Theory of Curves I

Details Chamber Structure and Wallcrossing in The ADHM Theory of Curves I Chamber Structure and Wallcrossing in The ADHM Theory of Curves I

2009-04-28

arxiv.org/abs/0904.4451v4

J. Geom. Phys. 62 (2012) 523

Mathematics

Algebraic Geometry

51 pages, AMS Latex, version 2: partial rewriting, relation to prior existing work clarified, references added and some errors

Scientific paper

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.

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