Moduli of ADHM sheaves and the local Donaldson-Thomas theory

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Abstract

The ADHM construction establishes a one-to-one correspondence between framed torsion free sheaves on the projective plane and stable framed representations of a quiver with relations in the category of complex vector spaces. This paper studies the geometry of moduli spaces of representations of the same quiver with relations in the abelian category of coherent sheaves on a smooth complex projective curve X. In particular it is proven that this moduli space is virtually smooth and related by relative Beilinson spectral sequence to the curve counting construction via stable pairs of Pandharipande and Thomas. This yields a new conjectural construction for the local Donaldson-Thomas theory of curves as well as a natural higher rank generalization.

Original languageEnglish (US)
Pages (from-to)763-799
Number of pages37
JournalJournal of Geometry and Physics
Volume62
Issue number4
DOIs
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

Keywords

  • ADHM construction
  • Donaldson-Thomas invariants
  • Moduli spaces of sheaves

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