Polynomial Bridgeland Stable Objects and Reflexive Sheaves

TL;DR

This paper classifies stable objects on smooth threefolds under polynomial Bridgeland stability, showing they are either Gieseker-stable sheaves or PT-stable objects, and explores their relation to reflexive sheaves.

Contribution

It proves a classification of moduli spaces of stable objects into two types under specific conditions and links these to reflexive sheaves.

Findings

Only two isomorphism types of moduli spaces exist under the given assumptions.

The intersection of PT-stable and dual-PT-stable moduli relates closely to reflexive sheaves.

The classification applies to smooth projective threefolds with certain stability vector conditions.

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.