Seminario de Álgebra Conmutativa, Geometría Algebraica y Geometría Aritmética

Jueves 29 de mayo a las 11:00 en el aula 420 del módulo 17, Departamento de Matemáticas de la UAM

Conferenciante: De-Qi Zhang (National University of Singapore)

Title: Morphisms from a very general hypersurface

Abstract: Let X be a very general hypersurface of degree d in the projective (n+1)-space with n > 2,

and f: X to Y a non-birational surjective morphism to a normal projective variety Y.

We first prove that Y is a klt Fano variety  if deg f > C for some constant C = C(n, d) depending only on n and d.

Next we prove an optimal upper bound: deg f is less than or equal to deg X,

provided that Y is factorial, deg f is prime and deg f > E(n) for some constant E(n).

As a corollary, we show that Y is the projective n-space under some conditions on Y and deg f. 

This is based on a joint work with Yongnam Lee and Yujie Luo.