Rationality of rationally connected threefolds admitting non-isomorphic endomorphisms

Abstract

We prove a structure theorem for non-isomorphic endomorphisms of weak Q-Fano threefolds, or more generally for threefolds with big anti-canonical divisor. Also provided is a criterion for a fibred rationally connected threefold to be rational. As a consequence, we show (without using the classification) that every smooth Fano threefold having a non-isomorphic surjective endomorphism is rational.

Transactions of the American Mathematical Society, to appear; 21 pages

References in corpus (3)

• Dynamics of Automorphisms of Compact Complex Manifolds
• Fano Varieties with Large Degree Endomorphisms
• Toward the second main theorem on complements: from local to global