Weak Approximation for Low Degree del Pezzo Surfaces

preprint2011arXivOpen access

Abstract

Let K=K(C)K = K(C) be the function field of a smooth curve CC. Applying the result of [Xu08], we prove that if S/KS/K is a degree one or two del Pezzo surface which can be completed to a generic family in the parametrizing space over CC, then weak approximation holds at every place c∈Cc \in C.

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