Polarized endomorphisms of uniruled varieties (with Appendix by Y. Fujimoto and N. Nakayama)

Abstract

We show that polarized endomorphisms of rationally connected threefolds with at worst terminal singularities are equivariantly built up from those on Q-Fano threefolds, Gorenstein log del Pezzo surfaces and P^1. Similar results are obtained for polarized endomorphisms of uniruled threefolds and fourfolds. As a consequence, we show that every smooth Fano threefold with a polarized endomorphism of degree > 1, is rational.

Compositio Mathematica (to appear)

References in corpus (6)

• Questions on self maps of algebraic varieties
• Building blocks of etale endomorphisms of complex projective manifolds
• Dynamics of Automorphisms of Compact Complex Manifolds
• Fano Varieties with Large Degree Endomorphisms
• Holomorphic self-maps of singular rational surfaces
• Polarized endomorphisms of complex normal varieties

Cited by in corpus (10)

• The volume of an isolated singularity
• Comparison of dynamical degrees for semi-conjugate meromorphic maps
• Non-isomorphic endomorphisms of Fano threefolds
• Surjective endomorphisms of projective surfaces: the existence of infinitely many dense orbits
• Amplified endomorphisms of Fano fourfolds
• Wild automorphisms of projective varieties, the maps which have no invariant proper subsets
• Int-amplified endomorphisms of compact Kähler spaces
• Invariant hypersurfaces of endomorphisms of projective varieties
• Totally invariant divisors of int-amplified endomorphisms of normal projective varieties
• Advances in the equivariant minimal model program and their applications in complex and arithmetic dynamics