Elliptic Subfields and Automorphisms of Genus 2 Function Fields

Tanush Shaska and Helmut Völklein

A chapter in Algebra, Arithmetic and Geometry with Applications, 2004, pp 703-723 from Springer

Abstract: Abstract We study genus 2 function fields with elliptic subfields of degree 2. The locus ℒ2 of these fields is a 2-dimensional subvariety of the moduli space M 2 of genus 2 fields. An equation for ℒ2 is already in the work of Clebsch and Bolza. We use a birational parameterization of ℒ2 by affine 2-space to study the relation between the j-invariants of the degree 2 elliptic subfields. This extends work of Geyer, Gaudry, Stichtenoth and others. We find a 1-dimensional family of genus 2 curves having exactly two isomorphic elliptic subfields of degree 2; this family is parameterized by the j-invariant of these subfields.

Keywords: Modulus Space; Automorphism Group; Elliptic Curf; Central Extension; Weierstrass Point (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18487-1_42

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DOI: 10.1007/978-3-642-18487-1_42

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