Plucker-Clebsch formula in higher dimension

2010/01/27 by Ciliberto, Ciro, Di Gennaro, Vincenzo
#14J99 #14M20 #14N15 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1001.4874

Abstract

Let S⊂\Ps^r (r≥ 5) be a nondegenerate, irreducible, smooth, complex, projective surface of degree d. Let δ_S be the number of double points of a general projection of S to \Ps⁴. In the present paper we prove that δ_S≤\binom d-2 2, with equality if and only if S is a rational scroll. Extensions to higher dimensions are discussed.

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