Tag - Fano varieties

Marcello Bernardara: Fano of K3 Type: Isomorphisms and classification of Hodge structures and K3 categories

13th May, 2021

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.

Paul Seidel: Fukaya categories of Calabi-Yau hypersurfaces

9th April, 2018

Consider a Calabi-Yau manifold which arises as a member of a Lefschetz pencil of anticanonical hypersurfaces in a Fano variety. The Fukaya categories of such manifolds have particularly nice properties. I will review this (partly still conjectural) picture, and how it constrains the field of definition of the Fukaya category.

Caucher Birkar: Singularities and Fano varieties in birational geometry

29th April, 2017

Fano varieties constitute a fascinating class of algebraic varieties that are important in birational
geometry and beyond. On the other hand, studying mild singularities is an indispensable feature of
modern birational geometry. In this talk I will try to explain how one interwines the two subjects to
prove various local and global boundedness statements regarding linear systems on varieties and
families of Fano varieties.