22 jun 2016 -- 15:45
Aula di Consiglio, Dip.Matematica, Università "La Sapienza", Roma
Abstract.
Given an n-dimensional smooth hypersurface X of degree d in projective n-space, it is elementary that X cannot be rational when d>n+1, but it is interesting to ask "how irrational" such a hypersurface can be. We discuss various measures of irrationality, and show that they are governed by positivity properties of the canonical bundle. Among other things, we prove a conjecture of Bastianelli, Cortina and De Poi concerning the least degree with which X can be expressed as a rational covering of projective space. This is joint work with Ein and Ullery.