Topics on Fano varieties of K3 type

TL;DR

This survey explores recent advances in the geometry of Fano varieties of K3 type, emphasizing their Hodge-theoretical aspects and links to hyperkähler geometry.

Contribution

It compiles and discusses recent results on Fano varieties of K3 type, highlighting their Hodge structures and connections to hyperkähler geometry.

Findings

Fano varieties of K3 type have rich Hodge-theoretical properties.

There are significant links between these Fano varieties and hyperkähler manifolds.

Recent results reveal new geometric and algebraic structures in this class.

Abstract

This is a survey paper about a selection of recent results on the geometry of a special class of Fano varieties, which are called of K3 type. The focus is mostly Hodge-theoretical, with an eye towards the multiple connections between Fano varieties of K3 type and hyperk\"ahler geometry.