AND THE ARITHMETIC OF A FAMILY OF NON-HYPERELLIPTIC CURVES OF GENUS 3

DOI10.1017/fmp.2014.2zbMath1346.14058OpenAlexW1992816268MaRDI QIDQ5496779

Jack A. Thorne

Publication date: 28 January 2015

Published in: Forum of Mathematics, Pi (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/fmp.2014.2

zbMATH Keywords

rational pointsfamilyaverage sizegenus 3plane quartichyperflexSelmer sets

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Rational points (14G05) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)]

Related Items (9)

The average size of the 2-Selmer group of a family of non-hyperelliptic curves of genus 3 ⋮ Arithmetic statistics of Prym surfaces ⋮ 2-Selmer groups of even hyperelliptic curves over function fields ⋮ The average size of the 3‐isogeny Selmer groups of elliptic curves y2=x3+k ⋮ Most odd-degree binary forms fail to primitively represent a square ⋮ Generalized Jacobians and explicit descents ⋮ $2$-Selmer groups of hyperelliptic curves with marked points ⋮ On the average number of 2-Selmer elements of elliptic curves over \(\mathbb F_q(X)\) with two marked points ⋮ On the arithmetic of simple singularities of type \(E\)

Cites Work

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• On invariant theory of \(\theta\)-groups
• On the moduli space of pointed algebraic curves of low genus: a computational approach
• Vinberg's representations and arithmetic invariant theory
• Two-cover descent on hyperelliptic curves
• Local Bounds for Torsion Points on Abelian Varieties

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