Equidistribution of periodic points of some automorphisms on K3 surfaces

TL;DR

This paper establishes the equidistribution of periodic points for certain automorphisms on K3 surfaces by constructing polarizable dynamical systems and applying Yuan's equidistribution results for small points.

Contribution

It introduces a method to build polarizable dynamical systems on K3 surfaces involving automorphisms and their inverses, demonstrating equidistribution of periodic points.

Findings

Periodic points are equidistributed on K3 surfaces under the constructed automorphisms.

A new approach to polarizable dynamical systems on complex surfaces.

Application of Yuan's work to automorphisms on K3 surfaces.

Abstract

We say (W, \{\phi_1,..., \phi_t\}) is a polarizable dynamical system of several morphisms if \phi_i are endomorphisms on a projective variety $W$ such that \bigotimes \phi_i^*L is linearly equivalent to L^q} for some ample line bundle L on W and for some q>t. If q is a rational number, then we have the equidistribution of small points of given dynamical system because of Yuan's work. As its application, we can build a polarizable dynamical system of an automorphism and its inverse on $K3$ surface and show its periodic points are equidistributed.