Polarized endomorphisms of log Calabi-Yau pairs

Algebraic Geometry Seminar

Organizers：

Caucher Birkar，Jia Jia 贾甲

Speaker：

José Ignacio Yáñez (UCLA)

Time：

Fri., 10:00-11:00 am, April 25, 2025

Online：

Zoom Meeting ID: 262 865 5007

Passcode: YMSC

Polarized endomorphisms of log Calabi-Yau pairs

An endomorphism on a normal projective variety X is said to be polarized if the pullback of an ample divisor A is linearly equivalent to qA, for some integer q>1. Examples of these endomorphisms are naturally found in toric varieties and abelian varieties. Indeed, it is conjectured that if X admits a polarized endomorphism, then X is a finite quotient of a toric fibration over an abelian variety. In this talk, we will restrict to the case of log Calabi-Yau pairs (X,B). We prove that if (X,B) admits a polarized endomorphism that preserves the boundary structure, then (X,B) is a finite quotient of a toric log Calabi-Yau fibration over an abelian variety. This is joint work with Joaquin Moraga and Wern Yeong.

About the Speaker:

I am a Hedrick Assistant Adjunct Professor at the Mathematics Department at UCLA under the mentorship of Joaquín Moraga.

I am interested in Algebraic Geometry, more precisely in Birational Algebraic Geometry. In particular, I am interested in applications of the Minimal Model Program, automorphisms and birational automorphisms of varieties, numerical dimension of divisors, and the Kawamata - Morrison conjecture.

I obtained my PhD in Mathematics at the University of Utah under the supervision of Christopher Hacon.

Before that, I got my Bachelor's and Master's degree in Mathematics at Universidad Católica de Chile under the supervision of Giancarlo Urzúa.