Seminario Álgebra Geometría Algebraica y Aritmética
Morphisms from a very general hypersurface
Ponente: De-Qi Zhang (National University of Singapore)Fecha: jueves 29 de mayo de 2025 - 11:00Lugar: Aula 420, Módulo 17, Departamento de Matemáticas, UAM
Resumen:
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.
