Plucker-Clebsch formula in higher dimension

Details Plucker-Clebsch formula in higher dimension Plucker-Clebsch formula in higher dimension

2010-01-27

arxiv.org/abs/1001.4874v1

Mathematics

Algebraic Geometry

12 pages

Scientific paper

Let $S\subset\Ps^r$ ($r\geq 5$) be a nondegenerate, irreducible, smooth,
complex, projective surface of degree $d$. Let $\delta_S$ be the number of
double points of a general projection of $S$ to $\Ps^4$. In the present paper
we prove that $ \delta_S\leq{\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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