Communications in Number Theory and Physics

Volume 4 (2010)

Number 2

Rank two ADHM invariants and wallcrossing

Pages: 417 – 461

DOI: https://dx.doi.org/10.4310/CNTP.2010.v4.n2.a4

Authors

W.Y. Chuang (NHETC, Rutgers University, New Jersey, U.S.A.)

D.E. Diaconescu (NHETC, Rutgers University, New Jersey, U.S.A.)

Guang Pan (NHETC, Rutgers University, New Jersey, U.S.A.)

Abstract

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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Published 1 January 2010