Journal article

### Homogeneous Spaces and Degree 4 del Pezzo Surfaces.

Abstract:

It is known that, given a genus 2 curve C : y^2 = f(x), where f(x) is quintic and defined over a field K, of characteristic different from 2, and given a homogeneous space H_delta for complete 2-descent on the Jacobian of C, there is a V_delta (which we shall describe), which is a degree 4 del Pezzo surface defined over K, such that H_delta(K) nonempty implies V_delta(K) nonempty. We shall prove that every degree 4 del Pezzo surface V, defined over K, arises in this way; furthermore, we shall...

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### Authors

Publisher:
Springer
Publication date:
2009-01-01
UUID:
uuid:5f634b4d-8dde-48c7-af9b-a814bbbd02fd
Local pid:
oai:eprints.maths.ox.ac.uk:803
Deposit date:
2011-05-20