Título inglés | Families of elliptic curves with genus 2 covers of degree 2. |
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Título español | Familias de curvas elípticas con recubrimientos de género 2 y de grado 2. |
Autor/es | Diem, Claus |
Organización | Fak. Math. Informat. Univ. Leipzig, Leipzig, Alemania |
Revista | 0010-0757 |
Publicación | 2006, 57 (1): 1-25, 18 Ref. |
Tipo de documento | articulo |
Idioma | Inglés |
Resumen inglés | We study genus 2 covers of relative elliptic curves over an arbitrary base in which 2 is invertible. Particular emphasis lies on the case that the covering degree is 2. We show that the data in the "basic construction" of genus 2 covers of relative elliptic curves determine the cover in a unique way (up to isomorphism). A classical theorem says that a genus 2 cover of an elliptic curve of degree 2 over a field of characteristic ≠ 2 is birational to a product of two elliptic curves over the projective line. We formulate and prove a generalization of this theorem for the relative situation. We also prove a Torelli theorem for genus 2 curves over an arbitrary base. |
Clasificación UNESCO | 120101 |
Palabras clave español | Curvas algebraicas ; Curvas elípticas |
Código MathReviews | MR2206178 |
Código Z-Math | Zbl 1100.14023 |
Acceso al artículo completo |