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

Claus Diem

Collectanea Mathematica (2006)

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

Abstract

top
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

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.