A speciality theorem for curves in $\bold P^5$
| dc.creator | Di Gennaro, Vincenzo | |
| dc.creator | Franco, Davide | |
| dc.date | 2005-07-07 | |
| dc.date.accessioned | 2026-07-07T05:21:31Z | |
| dc.date.available | 2026-07-07T05:21:31Z | |
| dc.description | Let $C\subset \bold P^r$ be an integral projective curve. One defines the speciality index $e(C)$ of $C$ as the maximal integer $t$ such that $h^0(C,ω_C(-t))>0$, where $ω_C$ denotes the dualizing sheaf of $C$. Extending a classical result of Halphen concerning the speciality of a space curve, in the present paper we prove that if $C\subset \bold P^5$ is an integral degree $d$ curve not contained in any surface of degree $< s$, in any threefold of degree $<t$, and in any fourfold of degree $<u$, and if $d>>s>>t>>u\geq 1$, then $ e(C)\leq {\frac{d}{s}}+{\frac{s}{t}}+{\frac{t}{u}}+u-6. $ Moreover equality holds if and only if $C$ is a complete intersection of hypersurfaces of degrees $u$, ${\frac{t}{u}}$, ${\frac{s}{t}}$ and ${\frac{d}{s}}$. We give also some partial results in the general case $C\subset \bold P^r$, $r\geq 3$. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0507162 | |
| dc.identifier | http://arxiv.org/abs/math/0507162 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75719 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14N15; 14H99; 14M10 | |
| dc.title | A speciality theorem for curves in $\bold P^5$ | |
| dc.type | text |