Polynomial Bridgeland stability conditions and the large volume limit

Details Polynomial Bridgeland stability conditions and the large volume limit Polynomial Bridgeland stability conditions and the large volume limit

2007-12-07

arxiv.org/abs/0712.1083v3

Geom. Topol., 2009, 13, 2389-2425

Mathematics

Algebraic Geometry

v3: minor revisions; v2: Acknowledgment added; 31 pages, 6 figures

Scientific paper

10.2140/gt.2009.13.2389

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.

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