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.
CILIBERTO, CIRO;DI GENNARO, VINCENZO
2004-01-01
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 $nI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.