Kawaguchi-Silverman conjecture for endomorphisms on rationally connected varieties admitting an int-amplified endomorphism

TL;DR

This paper proves the Kawaguchi-Silverman conjecture for all surjective endomorphisms on smooth rationally connected varieties that admit an int-amplified endomorphism, advancing understanding in algebraic dynamics.

Contribution

It establishes the conjecture for a broad class of varieties with specific endomorphism properties, filling a significant gap in the field.

Findings

Kawaguchi-Silverman conjecture holds for these varieties.

Surjective endomorphisms on such varieties exhibit predictable dynamical behavior.

The result applies to all smooth rationally connected varieties with an int-amplified endomorphism.

Abstract

We prove Kawaguchi-Silverman conjecture for all surjective endomorphisms on every smooth rationally connected variety admitting an int-amplified endomorphism.