Serre-invariant stability conditions and cubic threefolds

Abstract: Stability conditions on the Kuznetsov component of a Fano threefold of Picard rank 1, index 1 and 2 have been constructed by Bayer, Lahoz, Macrì and Stellari, making possible to study moduli spaces of stable objects and their geometric properties. In this talk we investigate the action of the Serre functor on these stability conditions. In the index 2 case and in the case of GM threefolds, we show that they are Serre-invariant. Then we prove a general criterion which ensures the existence of a unique Serre-invariant stability condition and applies to some of these Fano threefolds. Finally, we apply these results to the study of moduli spaces in the case of a cubic threefold X. In particular, we prove the smoothness of moduli spaces of stable objects in the Kuznetsov component of X and the irreducibility of the moduli space of stable Ulrich bundles on X. These results come from joint works with Song Yang and with Soheyla Feyzbakhsh and in preparation with Ethan Robinett.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

Free Mathematics Seminar

Series comments: This is the free mathematics seminar. Free as in freedom. We use only free and open source software to run the seminar.

The link to each week's talk is sent to the members of the e-mail list. The registration link to this mailing list is available on the homepage of the seminar.