Complete Linear Series on a Hyperelliptic Curve
| dc.creator | Park, Euisung | |
| dc.date | 2008-08-01 | |
| dc.date.accessioned | 2026-07-07T09:54:16Z | |
| dc.date.available | 2026-07-07T09:54:16Z | |
| dc.description | In this paper we study complete linear series on a hyperelliptic curve $C$ of arithmetic genus $g$. Let $A$ be the unique line bundle on $C$ such that $|A|$ is a $g^1_2$, and let $\mathcal{L}$ be a line bundle on $C$ of degree $d$. Then $\mathcal{L}$ can be factorized as $\mathcal{L} = A^m \otimes B$ where $m$ is the largest integer satisfying $H^0 (C,\mathcal{L} \otimes A^{-m}) \neq 0$. Let $b = {deg}(B)$. We say that \textit{the factorization type of} $\mathcal{L}$ is $(m,b)$. Our main results in this paper assert that $(m,b)$ gives a precise answer for many natural questions about $\mathcal{L}$. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/0808.0113 | |
| dc.identifier | http://arxiv.org/abs/0808.0113 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166249 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H99; 13D02; 14N05 | |
| dc.title | Complete Linear Series on a Hyperelliptic Curve | |
| dc.type | text |