Polynomial Bridgeland Stable Objects and Reflexive Sheaves

Abstract

On a smooth projective threefold, we show that there are only two isomorphism types for the moduli of stable objects with respect to Bayer's standard polynomial Bridgeland stability - the moduli of Gieseker-stable sheaves and the moduli of PT-stable objects - under the following assumptions: no two of the stability vectors are collinear, and the degree and rank of the objects are relatively prime. We also describe a close relation between the intersection of the moduli spaces of PT-stable and dual-PT-stable objects, and the moduli of reflexive sheaves.

13 pages. Introduction expanded, and other corrections and changes made according to referee's comments. Statements of Theorem 1.2 and Proposition 4.3 slightly modified. To appear in Math. Res. Lett