Degrees of Curves in Abelian Varieties

Details Degrees of Curves in Abelian Varieties Degrees of Curves in Abelian Varieties

1992-10-13

arxiv.org/abs/alg-geom/9210005v1

Mathematics

Algebraic Geometry

17 pages, PlainTex 1.2

Scientific paper

The degree of a curve $C$ in a polarized abelian variety $(X,\lambda)$ is the integer $d=C\cdot\lambda$. When $C$ generates $X$, we find a lower bound on $d$ which depends on $n$ and the degree of the polarization $\lambda$. 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.

Affiliated with

Also associated with

No associations

Rating

Degrees of Curves in Abelian Varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Degrees of Curves in Abelian Varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Degrees of Curves in Abelian Varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-510084