Hurwitz spaces of genus 2 covers of an elliptic curve.

Título inglés	Hurwitz spaces of genus 2 covers of an elliptic curve.
Título español	Espacios de Hurwitz de recubrimientos de género 2 de una curva elíptica.
Autor/es	Kani, Ernst
Organización	Dep. Math. Stat. Queen's Univ., Kingston (Ontario), Canadá
Revista	0010-0757
Publicación	2003, 54 (1): 1-51, 35 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	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.
Clasificación UNESCO	120101 ; 121014
Palabras clave español	Recubrimientos topológicos ; Curvas ; Espacio de Moduli ; Variedades topológicas
Código MathReviews	MR1962943
Código Z-Math	Zbl 1077.14529
Acceso al artículo completo