- journal article metadata
European Mathematical Society Publishing House
2017-03-24 14:03:38
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
33
2017
1
Twists of non-hyperelliptic curves
Elisa
Lorenzo García
Université de Rennes I, RENNES CEDEX, FRANCE
Twists, non-hyperelliptic curves, Galois embedding problems
In this paper we present a method for computing the set of twists of a non-singular projective curve defined over an arbitrary (perfect) field $k$. The method is based on a correspondence between twists and solutions to a Galois embedding problem. When in addition, this curve is non-hyperelliptic we show how to compute equations for the twists. If $k=\mathbb{F}_q$ the method then becomes an algorithm, since in this case, it is known how to solve the Galois embedding problems that appear. As an example we compute the set of twists of the non-hyperelliptic genus 6 curve $x^7-y^3-1=0$ when we consider it defined over a number field such that $[k(\zeta_{21}):k]=12$. For each twist equations are exhibited.
Number theory
Field theory and polynomials
Algebraic geometry
169
182
10.4171/RMI/931
http://www.ems-ph.org/doi/10.4171/RMI/931