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.
Citation
Arend Bayer. "Polynomial Bridgeland stability conditions and the large volume limit." Geom. Topol. 13 (4) 2389 - 2425, 2009. https://doi.org/10.2140/gt.2009.13.2389
Information