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Hurwitz spaces of genus 2 covers of an elliptic curve.

Ernst Kani — 2003

Collectanea Mathematica

Let E be an elliptic curve over a field K of characteristic not equal to 2 and let N > 1 be an integer prime to char(K). The purpose of this paper is to construct the (two-dimensional) Hurwitz moduli space H (E/K,N,2) which classifies genus 2 covers of E of degree N and to show that it is closely related to the modular curve X(N) which parametrizes elliptic curves with level-N-structure. More precisely, we introduce the notion of a normalized genus 2 cover of E/K and show that the corresponding...

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