Endomorphisms of hypersurfaces and other manifolds

2000/08/28 by Arnaud Beauville, A. Beauville, Beauville, A. · 3 citations
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #math.AG

paper · pdf · doi:10.48550/arxiv.math/0008205

5 pages, Plain TeX

arxiv created 2000/08/28 · openalex publication_date 2000/08/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a smooth hypersurface of degree >2 and dimension >1 admits no endomorphism of degree >1 (for hyperquadrics this is due to Paranjape and Srinivas). We then collect some general results on endomorphisms of projective manifolds; we prove in particular that ramified endomorphisms occur only on varieties of negative Kodaira dimension, and we classify those Del Pezzo surfaces which admit such endomorphism.

Cited by

• Frobenius liftable hypersurfaces
• Images of toric variety and amplified endomorphism of weak Fano threefolds
• Quasi-canonical lifting of projective varieties in positive characteristic

Related

• Endomorphisms of projective varieties
• Endomorphisms of hypersurfaces of Fano manifolds of Picard number 1
• Endomorphisms of singular del Pezzo surfaces
• Towards Characterizing Morphisms Between High Dimensional Hypersurfaces
• Endomorphisms of varieties and Bott vanishing