# 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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topDiem, 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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