Canonical map of low codimensional subvarieties
| dc.creator | Beorchia, Valentina | |
| dc.creator | Ciliberto, Ciro | |
| dc.creator | Di Gennaro, Vincenzo | |
| dc.date | 2004-03-12 | |
| dc.date.accessioned | 2026-07-07T05:06:20Z | |
| dc.date.available | 2026-07-07T05:06:20Z | |
| dc.description | Fix integers $a\geq 1$, $b$ and $c$. We prove that for certain projective varieties $V\subset{\bold P}^r$ (e.g. certain possibly singular complete intersections), there are only finitely many components of the Hilbert scheme parametrizing irreducible, smooth, projective, low codimensional subvarieties $X$ of $V$ such that $$ h^0(X,\Cal O_X(aK_X-bH_X)) \leq λd^{ε_1}+c(\sum_{1\leq h < ε_2}p_g(X^{(h)})), $$ where $d$, $K_X$ and $H_X$ denote the degree, the canonical divisor and the general hyperplane section of $X$, $p_g(X^{(h)})$ denotes the geometric genus of the general linear section of $X$ of dimension $h$, and where $λ$, $ε_1$ and $ε_2$ are suitable positive real numbers depending only on the dimension of $X$, on $a$ and on the ambient variety $V$. In particular, except for finitely many families of varieties, the canonical map of any irreducible, smooth, projective, low codimensional subvariety $X$ of $V$, is birational. | |
| dc.description | 31 pages | |
| dc.identifier | https://arxiv.org/abs/math/0403205 | |
| dc.identifier | http://arxiv.org/abs/math/0403205 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70434 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14C05, 14M07, 14M10 primary, 14J99 secondary | |
| dc.title | Canonical map of low codimensional subvarieties | |
| dc.type | text |