Approximation at places of bad reduction for rationally connected varieties

Brendan Hassett, Yuri Tschinkel

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Abstract

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 languageEnglish (US)
Pages (from-to)743-766
Number of pages24
JournalPure and Applied Mathematics Quarterly
Volume4
Issue number3 PART 2
StatePublished - Dec 17 2008

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ASJC Scopus subject areas

  • Mathematics(all)

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