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This is the second in a series of papers in which we study the n-Selmer groupof an elliptic curve.  In this paper, we show how to realize elements of the n-Selmer groupexplicitly as curves of degree n embedded in P^{n-1}. The main tool we use is acomparison between an easily obtained embedding into P^{n^2-1} and another mapinto P^{n^2-1} that factors through the Segre embedding P^{n-1} x P^{n-1} -->P^{n^2-1}. The comparison relies on an explicit version of the local-to-globalprinciple for the n-torsion of the Brauer group of the base field.Comment: 24 page

Explicit n-descent on elliptic curves, II. Geometry