Algebra and Geometry Seminar

USC, KAP 427

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.