Bridgeland Stability on Blow Ups and Counterexamples

Abstract

We give further counterexamples to the conjectural construction of Bridgeland stability on threefolds due to Bayer, Macrì, and Toda. This includes smooth projective threefolds containing a divisor that contracts to a point, and Weierstraß elliptic Calabi-Yau threefolds. Furthermore, we show that if the original conjecture, or a minor modification of it, holds on a smooth projective threefold, then the space of stability conditions is non-empty on the blow up at an arbitrary point. More precisely, there are stability conditions on the blow up for which all skyscraper sheaves are semistable.

15 pages, with appendix by Omprokash Das

References in corpus (2)

• Stability conditions on product threefolds of projective spaces and Abelian varieties
• Stability conditions, Bogomolov-Gieseker type inequalities and Fano 3-folds

Cited by in corpus (7)

• Stability conditions in families
• Derived categories and the genus of space curves
• Stability conditions on threefolds with nef tangent bundles
• Walls and asymptotics for Bridgeland stability conditions on 3-folds
• Stability conditions on Calabi-Yau double/triple solids
• Stability condition on Calabi-Yau threefold of complete intersection of quadratic and quartic hypersurfaces
• Tilt stability and the degree of irrationality of surfaces on threefolds