Michal Kapustka

Title: Nodal Gushel Mukai fourfolds

Abstract: 
Gushel Mukai fourfold i.e. fourfolds obtained as quadratic sections of a 
cone over the Grassmannian G(2,5) are among the most interesting 
Fano fourfolds, in particular from the point of view of rationality problems. 
We discuss the geometry of nodal Gushel Mukai fourfolds. We prove that 
such fourfolds are birational to Verra fourfolds (quadric sections of a cone 
over P^2xP^2) and study associated quadric fibration structures on them. 
This is joint work in progress with G. Bini, G. Kapustka and R. Laterveer.