Bridgeland stability on blow ups and counterexamples

Cristian Martinez, Benjamin Schmidt

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7 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1495-1510
Number of pages16
JournalMathematische Zeitschrift
Volume292
Issue number3-4
DOIs
StatePublished - Aug 1 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics

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