Projective varieties with many degenerate subvarieties
| dc.creator | Mezzetti, Emilia | |
| dc.date | 1993-03-20 | |
| dc.date.accessioned | 2026-07-07T09:05:48Z | |
| dc.date.available | 2026-07-07T09:05:48Z | |
| dc.description | We study the problem of classifying the irreducible projective varieties $X$ of dimension $n\ge 2$ in $\Bbb P^N$ which contain an algebraic family $\Cal F$ of dimension $h+1$ ($h<n$) of subvarieties $Y$ of dimension $n-h$, each one contained in a $\Bbb P^{N-h-1}$. We prove that one of the following happens: (i) there exists an integer $r$, $r<N-n$ such that $X$ is contained in a variety $V_r$ of dimension at most $N-r$ containing a family of dimension $h+1$ of subvarieties of dimension $N-h-r$, each one contained in a linear space of dimension $N-h-1$; (ii) The degree of $Y$ is bounded by a function of $h$ and $N-n$ (in this case $X$ is called of isolated type). Successively we study some special cases; in particular we give a complete classification of surfaces in $\Bbb P^5$ containing a family of dimension $2$ of curves of $\Bbb P^3$. | |
| dc.description | 19 pages, AMS-TeX 2.1 | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9303002 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9303002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149800 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Projective varieties with many degenerate subvarieties | |
| dc.type | text |