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Endomorphisms of hypersurfaces and other manifolds

A. Beauville
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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.

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A. Beauville. 2000-08-28. Endomorphisms of hypersurfaces and other manifolds. https://arxiv.org/abs/math/0008205

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