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arXiv · 1708.08567

Bridgeland Stability on Blow Ups and Counterexamples

Cristian Martinez·Benjamin Schmidt·Omprokash Das
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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.

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Cristian Martinez, Benjamin Schmidt, Omprokash Das. 2018-09-04. Bridgeland Stability on Blow Ups and Counterexamples. https://doi.org/10.1007/s00209-018-2149-3

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