On smooth rationally connected projective threefolds of Picard number two admitting int-amplified endomorphisms

TL;DR

This paper characterizes smooth rationally connected projective threefolds with Picard number two that admit int-amplified endomorphisms, showing they are toric, and explores properties of invariant curves under endomorphisms of projective three-space.

Contribution

It establishes a characterization of certain threefolds admitting int-amplified endomorphisms as toric, and analyzes invariant curves under endomorphisms of projective space.

Findings

Such threefolds are toric if and only if they admit an int-amplified endomorphism.

A totally invariant smooth curve under a non-isomorphic surjective endomorphism of P^3 must be a line if blowup-equivariant.

Provides conditions linking endomorphisms and geometric structures of threefolds.

Abstract

We prove that a smooth rationally connected projective threefold of Picard number two is toric if and only if it admits an int-amplified endomorphism. As a corollary, we show that a totally invariant smooth curve of a non-isomorphic surjective endomorphism of $\mathbb{P}^3$ must be a line when it is blowup-equivariant.