# Hurwitz spaces of genus 2 covers of an elliptic curve.

Collectanea Mathematica (2003)

- Volume: 54, Issue: 1, page 1-51
- ISSN: 0010-0757

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topKani, Ernst. "Hurwitz spaces of genus 2 covers of an elliptic curve.." Collectanea Mathematica 54.1 (2003): 1-51. <http://eudml.org/doc/42993>.

@article{Kani2003,

abstract = {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 moduli space H sub (E/K,N) is an open subset of (a twist of) X(N), and that the connected components of the Hurwitz space H(E/K,N,2) are of the form E x H sub (E'/K,N) for suitable elliptic curves E' ~ E and divisors M|N.},

author = {Kani, Ernst},

journal = {Collectanea Mathematica},

keywords = {Recubrimientos topológicos; Curvas; Espacio de Moduli; Variedades topológicas},

language = {eng},

number = {1},

pages = {1-51},

title = {Hurwitz spaces of genus 2 covers of an elliptic curve.},

url = {http://eudml.org/doc/42993},

volume = {54},

year = {2003},

}

TY - JOUR

AU - Kani, Ernst

TI - Hurwitz spaces of genus 2 covers of an elliptic curve.

JO - Collectanea Mathematica

PY - 2003

VL - 54

IS - 1

SP - 1

EP - 51

AB - 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 moduli space H sub (E/K,N) is an open subset of (a twist of) X(N), and that the connected components of the Hurwitz space H(E/K,N,2) are of the form E x H sub (E'/K,N) for suitable elliptic curves E' ~ E and divisors M|N.

LA - eng

KW - Recubrimientos topológicos; Curvas; Espacio de Moduli; Variedades topológicas

UR - http://eudml.org/doc/42993

ER -

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