Elliptic Subfields and Automorphisms of Genus 2 Function Fields

By Tanush Shaska, H. Voelklein. 2001

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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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d5500404009b1440ae836081a2ac2fd329692f58