Arnaud Beauville
Abstract
We prove that a smooth hypersurface of degree ≥ 3 in Pn(n≥3) 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 classify in particular those Del Pezzo surfaces which admit an endomorphism of degree > 1.
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We prove that a smooth hypersurface of degree ≥ 3 in Pn(n≥3) 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 classify in particular those Del Pezzo surfaces which admit an endomorphism of degree > 1.
Key concepts: Endomorphism, Mathematics, Hypersurface, Degree (music), Pure mathematics, Physics, Acoustics