Nondegenerate curves of low genus over small finite fields

Details Nondegenerate curves of low genus over small finite fields Nondegenerate curves of low genus over small finite fields

2009-07-12

arxiv.org/abs/0907.2060v1

Mathematics

Number Theory

8 pages; uses pstricks

Scientific paper

In a previous paper, we proved that over a finite field $k$ of sufficiently large cardinality, all curves of genus at most 3 over k can be modeled by a bivariate Laurent polynomial that is nondegenerate with respect to its Newton polytope. In this paper, we prove that there are exactly two curves of genus at most 3 over a finite field that are not nondegenerate, one over F_2 and one over F_3. Both of these curves have remarkable extremal properties concerning the number of rational points over various extension fields.

Affiliated with

Also associated with

No associations

Rating

Nondegenerate curves of low genus over small finite fields 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 Nondegenerate curves of low genus over small finite fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nondegenerate curves of low genus over small finite fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-593665