Let $S\subset\mathbb{P}^r$ ($r\geq 5$) 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 $\mathbb{P}^4$. 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.
Ciliberto, C., DI GENNARO, V. (2011). Plucker-Clebsch formula in higher dimension. In Commutative Algebra and its connections to Geometry. American Mathematical Society.
Plucker-Clebsch formula in higher dimension
CILIBERTO, CIRO;DI GENNARO, VINCENZO
2011-01-01
Abstract
Let $S\subset\mathbb{P}^r$ ($r\geq 5$) 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 $\mathbb{P}^4$. 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.File in questo prodotto:
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