Amplified endomorphisms of Fano fourfolds

Abstract

Let $X$ be a smooth Fano fourfold admitting a conic bundle structure. We show that $X$ is toric if and only if $X$ admits an amplified endomorphism; in this case, $X$ is a rational variety.

Minor revision. Final version, to appear in manuscripta mathematica

References in corpus (5)

• Questions on self maps of algebraic varieties
• On automorphism groups of fiber bundles
• Rigidity of rationally connected smooth projective varieties from dynamical viewpoints
• Quasi elementary contractions of Fano manifolds
• Non-isomorphic endomorphisms of Fano threefolds

Cited by in corpus (3)

• Rigidity of rationally connected smooth projective varieties from dynamical viewpoints
• Boundedness of finite morphisms onto Fano manifolds with large Fano index
• Advances in the equivariant minimal model program and their applications in complex and arithmetic dynamics