Clifford Index of ACM Curves in ${\mathbb P}^3$
| dc.creator | Hartshorne, Robin | |
| dc.date | 2001-04-27 | |
| dc.date.accessioned | 2026-07-07T04:41:29Z | |
| dc.date.available | 2026-07-07T04:41:29Z | |
| dc.description | In this paper we review the notions of gonality and Clifford index of an abstract curve. For a curve embedded in a projective space, we investigate the connection between the \ci of the curve and the \gc al properties of its \emb. In particular if $C$ is a curve of degree $d$ in $¶^3$, and if $L$ is a multisecant of maximum order $k$, then the pencil of planes through $L$ cuts out a $g^1_{d-k}$ on $C$. If the gonality of $C$ is equal to $d-k$ we say the gonality of $C$ can be computed by multisecants. We discuss the question whether the \go of every smooth ACM curve in $¶^3$ can be computed by multisecants, and we show the answer is yes in some special cases. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0104266 | |
| dc.identifier | http://arxiv.org/abs/math/0104266 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61381 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H45; 14H50; 14M06 | |
| dc.title | Clifford Index of ACM Curves in ${\mathbb P}^3$ | |
| dc.type | text |