Families of elliptic curves with genus 2 covers of degree 2

Autores: Claus Diem
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 57, Fasc. 1, 2006, págs. 1-25
Idioma: inglés
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Resumen
- We study genus 2 covers of relative elliptic curves over an arbitrary base in which 2 is in invertible. Particular emphasis lies on the case that the co 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 de degree 2 over a field of characteristic =/= 2 is birational to a product of two elliptic curves over the projective line. We formulate and pro prove a generalization of this theorem for the relative situation. We also pro prove a Torelli theorem for genus 2 curves over an arbitrary base.