Invariant hypersurfaces of endomorphisms of projective varieties

Abstract

We consider surjective endomorphisms f of degree > 1 on projective manifolds X of Picard number one and their f^{-1}-stable hypersurfaces V, and show that V is rationally chain connected. Also given is an optimal upper bound for the number of f^{-1}-stable prime divisors on (not necessarily smooth) projective varieties.

Advances in Mathematics (to appear)

References in corpus (3)

• Inversion of adjunction on log canonicity
• Questions on self maps of algebraic varieties
• Polarized endomorphisms of uniruled varieties (with Appendix by Y. Fujimoto and N. Nakayama)

Cited by in corpus (1)

• Int-amplified endomorphisms of compact Kähler spaces