TY - JOUR
T1 - Bridgeland stability on blow ups and counterexamples
AU - Martinez, Cristian
AU - Schmidt, Benjamin
N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/8/1
Y1 - 2019/8/1
N2 - 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.
AB - 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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U2 - 10.1007/s00209-018-2149-3
DO - 10.1007/s00209-018-2149-3
M3 - Article
AN - SCOPUS:85055501898
SN - 0025-5874
VL - 292
SP - 1495
EP - 1510
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 3-4
ER -