Endomorphisms of hypersurfaces and other manifolds

Details Endomorphisms of hypersurfaces and other manifolds Endomorphisms of hypersurfaces and other manifolds

2000-08-28

arxiv.org/abs/math/0008205v1

Mathematics

Algebraic Geometry

5 pages, Plain TeX

Scientific paper

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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