Degrees of Curves in Abelian Varieties
| dc.creator | Debarre, Olivier | |
| dc.date | 1992-10-13 | |
| dc.date.accessioned | 2026-07-07T09:05:46Z | |
| dc.date.available | 2026-07-07T09:05:46Z | |
| dc.description | The degree of a curve $C$ in a polarized abelian variety $(X,λ)$ is the integer $d=C\cdotλ$. When $C$ generates $X$, we find a lower bound on $d$ which depends on $n$ and the degree of the polarization $λ$. The smallest possible degree is $d=n$ and is obtained only for a smooth curve in its Jacobian with its principal polarization (Ran, Collino). The cases $d=n+1$ and $d=n+2$ are studied. Moreover, when $X$ is simple, it is shown, using results of Smyth on the trace of totally positive algebraic integers, that if $d\le 1.7719\, n$, then $C$ is smooth and $X$ is isomorphic to its Jacobian. We also get an upper bound on the geometric genus of $C$ in terms of its degree. | |
| dc.description | 17 pages, PlainTex 1.2 | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9210005 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9210005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149789 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Degrees of Curves in Abelian Varieties | |
| dc.type | text |