Weak approximation for cubic hypersurfaces

Abstract

We prove weak approximation for smooth cubic hypersurfaces of dimension at least $2$ defined over the function field of a complex curve.

Zhiyu Tian. "Weak approximation for cubic hypersurfaces." Duke Math. J. 164 (7) 1401 - 1435, 15 May 2015. https://doi.org/10.1215/00127094-2916322

Received: 22 May 2013; Revised: 27 July 2014; Published: 15 May 2015

First available in Project Euclid: 14 May 2015

MathSciNet: MR3347318

Digital Object Identifier: 10.1215/00127094-2916322

Subjects:

Primary: 14M22

Secondary: 14G05 , 14G27

Keywords: rationally connected varieties , weak approximation