This paper addresses weak approximation for rationally connected varieties defined over the function field of a curve, especially at places of bad reductiod. Our approach entails analyzing the rational connectivity of the smooth locus of singular reductions of the variety. As an application, we prove weak approximation for cubic surfaces and Fano hypersurfaces of dimension at least three, with square-free discriminant.
|Original language||English (US)|
|Number of pages||24|
|Journal||Pure and Applied Mathematics Quarterly|
|Issue number||3 PART 2|
|State||Published - Dec 17 2008|
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