Higher dimensional moduli spaces on Kuznetsov components of Fano threefolds
Laura Pertusi (Università degli Studi di Milano)
Tuesday 21st January 15:00-16:00 Maths 311B
Abstract
Stability conditions on the Kuznetsov component of a Fano threefold of Picard rank 1, index 1 or 2 have been constructed by Bayer, Lahoz, Macrì and Stellari, making possible to study moduli spaces of semistable objects and their geometric properties. Although small dimensional examples of moduli spaces are well-understood and are related to classical moduli spaces of stable sheaves on the threefold, the higher dimensional ones are more mysterious.
In this talk, we will show a non-emptiness result for these moduli spaces. Then we will focus on the case of cubic threefolds. When the dimension of the moduli space with respect to a primitive numerical class is larger than 5, we show that the Abel-Jacobi map from the moduli space to the intermediate Jacobian is surjective with connected fibers, and its general fiber is a smooth Fano variety with primitive canonical divisor. When the dimension is sufficiently large, we further show that the general fibers are stably birational to each other. This is a joint work with Chunyi Li, Yinbang Lin and Xiaolei Zhao.
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