In this talk, we introduce the infinitesimal categorical Torelli for Fano 3-folds. We obtain a commutative diagram connecting the infinitesimal spaces
of the geometric spaces and the categories. These are joint works with Jacovskis Augustinas, Zhiyu Liu, and Shizhuo Zhang. In a joint work with
Shizhuo Zhang, we give a simple new disproof of Kuznetsov's Fano 3-folds conjecture for degree 2 and index two Fano 3-fold based on infinitesimal
categorical Torelli theorems.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/158