Let $V\subset \bold P^4$ be a reduced and irreducible hypersurface of degree $k\geq 3$, whose singular locus consists of $\delta$ ordinary double points. In this paper we prove that if $\delta < k/2$, or the nodes of $V$ are set-theoretic intersection of hypersurfaces of degree $n<k/2$ and $\delta < (k-2n)(k-1)^2/k$, then any projective surface contained in $V$ is a complete intersection on $V$. In particular $V$ is ${\bold Q}$-factorial. We give more precise results for {\it {smooth}} surfaces contained in $V$.

Ciliberto, C., DI GENNARO, V. (2004). Factoriality of certain hypersurfaces of ${bold P^4}$ with ordinary double points.. In V. Popov (a cura di), Algebraic Transformation Groups and Algebraic Varieties (pp. 1-7). Springer.

### Factoriality of certain hypersurfaces of ${bold P^4}$ with ordinary double points.

#### Abstract

Let $V\subset \bold P^4$ be a reduced and irreducible hypersurface of degree $k\geq 3$, whose singular locus consists of $\delta$ ordinary double points. In this paper we prove that if $\delta < k/2$, or the nodes of $V$ are set-theoretic intersection of hypersurfaces of degree $n ##### Scheda breve Scheda completa Scheda completa (DC) Settore MAT/03 - Geometria English Rilevanza internazionale Capitolo o saggio Projective hypersurface, ordinary double point, complete intersection, space curve, Noether-Halphen theory, Weil divisor class group. http://www.springer.com/mathematics/algebra/book/978-3-540-20838-9 Ciliberto, C., DI GENNARO, V. (2004). Factoriality of certain hypersurfaces of${bold P^4}\$ with ordinary double points.. In V. Popov (a cura di), Algebraic Transformation Groups and Algebraic Varieties (pp. 1-7). Springer.
Ciliberto, C; DI GENNARO, V
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/31715
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