Fixed points of smooth varieties with Kodaira dimension zero

TL;DR

This paper investigates the behavior of fixed points under iterated endomorphisms on varieties with Kodaira dimension zero, extending known results from abelian varieties to broader classes.

Contribution

It introduces new estimates for fixed points on abelian varieties and generalizes these results to varieties of Kodaira dimension zero and their periodic subvarieties.

Findings

Established growth estimates for fixed points on abelian varieties.

Extended fixed point results to varieties with Kodaira dimension zero.

Analyzed periodic subvarieties under endomorphisms.

Abstract

In this paper, we study the growth of the number of fixed points from iterating an endomorphism of an abelian variety. Using the estimates obtained on an abelian variety, we are able to extend the results to endomorphisms on varieties of Kodaira dimension zero and more generally their periodic subvarieties.