Polynomial Bridgeland stability conditions and the large volume limit

Bayer, Arend¹

¹ Department of Mathematics, University of Utah, 155 South 1400 East, Room 233, Salt Lake City, UT 84112

Geometry & topology, Tome 13 (2009) no. 4, pp. 2389-2425.

Résumé

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.

Détail

DOI : 10.2140/gt.2009.13.2389

Keywords: stability condition, derived category, counting invariant, wall crossing, Donaldson–Thomas invariant

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