Linear determinantal representations of smooth plane cubics over finite fields
Algebraic Geometry
2016-04-22 v2 Number Theory
Abstract
In this note, we study linear determinantal representations of smooth plane cubics over finite fields. We give an explicit formula of linear determinantal representations corresponding to rational points. Using Schoof's formula, we count the number of projective equivalence classes of smooth plane cubics over a finite field admitting prescribed number of equivalence classes of linear determinantal representations. As an application, we determine isomorphism classes of smooth plane cubics over a finite field with 0, 1 or 2 equivalence classes of linear determinantal representations.
Keywords
Cite
@article{arxiv.1604.00115,
title = {Linear determinantal representations of smooth plane cubics over finite fields},
author = {Yasuhiro Ishitsuka},
journal= {arXiv preprint arXiv:1604.00115},
year = {2016}
}