Grassmannian geometry and Fano varieties of K3 type.

Seminario riservato al gruppo di ricerca, seconda parte. Subvarieties of Grassmannian (and especially Fano varieties) obtained from section of homogeneous vector bundles are far from being classified. A case of particular interest is given by the Fano varieties of K3 type, for their deep links with hyperk\"ahler geometry. In this talk we will give a survey of some recent techniques we developed to study the Hodge theory of this particular class of varieties, and we will present some new examples