Title: Nondegenerate curves of low genus over small finite fields
Authors: Castryck, Wouter * ×
Voight, John * #
Issue Date: 2010
Publisher: American Mathematical Society
Host Document: Contemporary Mathematics vol:521 pages:21-28
Series Title: Contemporary Mathematics
Conference: Arithmetic, Geometry, Cryptography and Coding Theory edition:12 location:Marseille (France) date:30 March - 3 April 2009
Abstract: 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 extremal properties concerning the number of rational points over various extension fields.
ISBN: 978-0-8218-4955-2
ISSN: 0271-4132
Publication status: published
KU Leuven publication type: IC
Appears in Collections:Algebra Section
* (joint) first author
× corresponding author
# (joint) last author

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