Rank Two ADHM Invariants and Wallcrossing

Details Rank Two ADHM Invariants and Wallcrossing Rank Two ADHM Invariants and Wallcrossing

2010-02-02

arxiv.org/abs/1002.0579v2

Commun. Numb. Th. Phys. 4 (2010) 417-461

Mathematics

Algebraic Geometry

27 pages, AMS LaTex; ver2: minor changes.

Scientific paper

Generalized Donaldson-Thomas invariants corresponding to local D6-D2-D0 configurations are defined applying the formalism of Joyce and Song to ADHM sheaves on curves. A wallcrossing formula for invariants of D6-rank two is proven and shown to agree with the wallcrossing formula of Kontsevich and Soibelman. Using this result, the asymptotic D6-rank two invariants of (-1,-1) and (0,-2) local rational curves are computed in terms of the D6-rank one invariants.

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