An implementation of two-cover descent on plane quartic curves

Author: 
File(s): 
Date created: 
2019-08-09
Identifier: 
etd20482
Supervisor(s): 
Nils Bruin
Department: 
Science: Department of Mathematics
Keywords: 
Rational points
Bitangents
Plane quartic curves
Descent methods
Abstract: 

We gather experimental evidence related to the question of deciding whether a smooth plane quartic curve has a rational point. Smooth plane quartics describe curves in genus 3, the first genus in which non-hyperelliptic curves occur. We present an algorithm that determines a set of unramified covers of a given plane quartic curve, with the property that any rational point will lift to one of the covers. In particular, if the algorithm returns the empty set, then the curve has no rational points. We apply our algorithm to a total of 1000 isomorphism classes of randomly-generated plane quartic curves.

Thesis type: 
(Thesis) M.Sc.
Document type: 
Thesis
Rights: 
This thesis may be printed or downloaded for non-commercial research and scholarly purposes. Copyright remains with the author.
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