Wall-crossings for Twisted Quiver Bundles

Details Wall-crossings for Twisted Quiver Bundles Wall-crossings for Twisted Quiver Bundles

2011-01-21

arxiv.org/abs/1101.4156v1

Mathematics

Algebraic Geometry

Scientific paper

Given a double quiver, we study homological algebra of twisted quiver sheaves with the moment map relation by modifying the short exact sequence of Gothen and King. Then in a certain one-parameter space of the stability conditions, we obtain a wall-crossing formula for the generalized Donaldson-Thomas invariants of the abelian category of framed twisted quiver sheaves on a smooth projective curve. To do so, we closely follow the approach of Chuang, Diaconescu, and Pan in the ADHM quiver case, which makes use of the theory of Joyce and Song. The invariants virtually count framed twisted quiver sheaves with the moment map relation.

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