Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Stronger Bogomolov—Gieseker inequality and Bridgeland stability conditions
The classical Bogomolov inequality gives a bound for the second Chern character of stable sheaves on smooth projective varieties. This thus implies the existence of the Bridgeland stability conditions on smooth surfaces by the tilting technique. However, to construct a Bridgeland stability condition on higher dimensional varieties, a Bogomolov—Gieseker type bound for higher Chern characters is expected, whose proof usually requires a stronger Bogomolov—Gieseker inequality. Besides Fano varieties and K3 surfaces, it is difficult to prove a stronger Bogomolov—Gieseker inequality. In this talk, I will show one way to prove such an inequality on some Calabi—Yau threefolds, and as an application, the existence of the Bridgeland stability conditions on such Calabi—Yau threefolds. If time permits, I will mention another application of this stronger inequality by Feyzbakhsh—Thomas on enumerative invariants.
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