学术报告（林汛 2025.10.16）

摘要： In this talk, I will study the infinitesimal Torelli for special Gushel-Mukai 3-folds, which are the double cover of rigid Fano 3-folds branched along K3 surfaces. The involution from the double cover breaks the infinitesimal period map of special Gushel-Mukai 3-folds into invariant part and the anti invariant part. Our theorems shows the invariant part of the infinitesimal period map is injective. The anti-invariant part has dimensional 3 kernel. Since the invariant of the infinitesimal period map represents the differential map from Moduli space of special Gushel-Mukai 3-folds to the period domain, we prove the infinitesimal Torelli for special Gushel-Mukai 3-folds. We have two methods, one is categorical, another one is geometric. For the categorical perspective, we use the theory of infinitesimal categorical Torelli developed by Augustinas, Xun Lin, Zhiyu Liu, and Shizhuo Zhang. Combining the categorical duality and the theory of Normal Hochschild cohomology developed by Kuznetsov, we are able to obtain the results. For the geometric perspective, we reduce the infinitesimal Torelli for special Gushel-Mukai 3-folds to the Twisted Torelli of K3 surfaces. Finally, if time permit, i will talk about the geometric explanation of our results. The results in the talk are based on joint work with Shizhuo Zhang and Zheng Zhang.