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Genus 2 curves that admit a degree 5 map to an elliptic curve
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Kay Magaard
Published/Copyright:
March 12, 2009
Abstract
We continue our study of genus 2 curves C that admit a cover C → E 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
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Articles in the same Issue
- On the classification of infinite-dimensional irreducible Hermitian-symmetric affine coadjoint orbits
- A partial generalization of the Helgason Conjecture to general bounded homogeneous domains
- Antisymmetric elements in group rings with an orientation morphism
- Gradient estimates for the eigenfunctions on compact manifolds with boundary and Hörmander Multiplier Theorem
- On loops rich in automorphisms that are abelian modulo the nucleus
- Minimal number of periodic points for C1 self-maps of compact simply-connected manifolds
- On a question of Bombieri and Bourgain
- Separate real analyticity and CR extendibility
- Coverings of Banach spaces: beyond the Corson theorem
- Genus 2 curves that admit a degree 5 map to an elliptic curve
