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Approximation at places of bad reduction

Research paper by Brendan Hassett, Yuri Tschinkel

Indexed on: 10 May '06Published on: 10 May '06Published in: Mathematics - Algebraic Geometry



Abstract

This paper addresses weak approximation for rationally connected varieties defined over the function field of a curve, especially at places of bad reduction. 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 with square-free discriminant.