Fano varieties of (derived) K3 type are Fano varieties whose Hodge structure (derived category) contains a K3-type sub-Hodge structure (subcategory). Many examples of such varieties are known, arising as zeroes of homogeneous bundles on Grassmannians, in dimensions that grow up to 19. In this talk, I will first present joint work with Fatighenti and Manivel showing that many of these examples can be related by geometric correspondences and have actually the same K3-type Hodge structure. I will also present an ongoing project with Fatighenti, Manivel and Tanturri, whose aim is to show that in the case of Fano fourfolds, the only possible K3-type structures which are not actual K3 can arise from Gushel-Mukai, cubics and Küchle c5 fourfolds.
This video is part of the COW Seminar series.
