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...Expand abstract
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Homogeneous Spaces and Degree 4 del Pezzo Surfaces.
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