Seminar Event Detail

Algebraic Geometry

Date:  Wednesday, December 07, 2016
Location:  4096 East Hall (4:10 PM to 5:30 PM)

Title:  Building blocks of polarized endomorphisms

Abstract:   An endomorphism f of a normal projective variety X is polarized if the pullback via f of an ample divisor H is linearly equivalent to qH for some q>1. Non-trivial endomorphisms on projective spaces or multiplication maps on Abelian varieties are examples of such maps. We show that for mildly singular X, we can run an f-equivariant minimal model program. As a result, the building blocks of polarized endomorphisms are those on Fano varieties of Picard number one and those on Abelian varieties (or their quasi-etale quotients). In particular, we show that (a power of) every polarized endomorphism of a smooth rationally connected variety acts as a scalar on the Neron-Severi group. This is a joint work with S. Meng.


Speaker:  De-Qi Zhang
Institution:  National University of Singapore

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