Polynomial Bridgeland stability conditions and the large volume limit

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Abstract

We introduce the notion of a polynomial stability condition, generalizing Bridgeland stability conditions on triangulated categories. We construct and study a family of polynomial stability conditions for any normal projective variety. This family includes both Simpson-stability and large volume limits of Bridgeland stability conditions.

We show that the PT/DT-correspondence relating stable pairs to Donaldson-Thomas invariants (conjectured by Pandharipande and Thomas) can be understood as a wall-crossing in our family of polynomial stability conditions. Similarly, we show that the relation between stable pairs and invariants of one-dimensional torsion sheaves (proven recently by the same authors) is a wall-crossing formula.

Original languageEnglish
Pages (from-to)2389-2425
Number of pages37
JournalGeometry and Topology
Volume13
Issue number4
DOIs
Publication statusPublished - 2009

Keywords

  • stability condition
  • derived category
  • counting invariant
  • wall crossing
  • Donaldson–Thomas invariant

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