# Families of elliptic curves with genus 2 covers of degree 2.

Collectanea Mathematica (2006)

• Volume: 57, Issue: 1, page 1-25
• ISSN: 0010-0757

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## Abstract

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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.

## How to cite

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Diem, Claus. "Families of elliptic curves with genus 2 covers of degree 2.." Collectanea Mathematica 57.1 (2006): 1-25. <http://eudml.org/doc/41808>.

@article{Diem2006,
abstract = {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.},
author = {Diem, Claus},
journal = {Collectanea Mathematica},
keywords = {Curvas algebraicas; Curvas elípticas; cover; genus 2 curve; Hurwitz space; -bundle},
language = {eng},
number = {1},
pages = {1-25},
title = {Families of elliptic curves with genus 2 covers of degree 2.},
url = {http://eudml.org/doc/41808},
volume = {57},
year = {2006},
}

TY - JOUR
AU - Diem, Claus
TI - Families of elliptic curves with genus 2 covers of degree 2.
JO - Collectanea Mathematica
PY - 2006
VL - 57
IS - 1
SP - 1
EP - 25
AB - 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.
LA - eng
KW - Curvas algebraicas; Curvas elípticas; cover; genus 2 curve; Hurwitz space; -bundle
UR - http://eudml.org/doc/41808
ER -

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