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Licensed Unlicensed Requires Authentication Published by De Gruyter March 12, 2009

Genus 2 curves that admit a degree 5 map to an elliptic curve

Kay Magaard, Tanush Shaska and Helmut Völklein
From the journal

Abstract

We continue our study of genus 2 curves C that admit a cover CE to a genus 1 curve E of prime degree n. These curves C form an irreducible 2-dimensional subvariety ℒn of the moduli space ℳ2 of genus 2 curves. Here we study the case n = 5. This extends earlier work for degree 2 and 3, aimed at illuminating the theory for general n.

We compute a normal form for the curves in the locus ℒ5 and its three distinguished subloci. Further, we compute the equation of the elliptic subcover in all cases, give a birational parametrization of the subloci of ℒ5 as subvarieties of ℳ2 and classify all curves in these loci which have extra automorphisms.

Received: 2007-03-09
Published Online: 2009-03-12
Published in Print: 2009-May

© de Gruyter 2009