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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Weak approximation for low degree Del Pezzo surfaces

Author: Chenyang Xu
Journal: J. Algebraic Geom. 21 (2012), 753-767
Published electronically: January 18, 2012
MathSciNet review: 2957695
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Abstract | References | Additional Information

Abstract: Let $K=\textrm {Func}(C)$ be the function field of a smooth curve $C$. For every Del Pezzo surface $S/K$ which is an appropriately generic, weak approximation for $S$ holds at every place of $K$, i.e., for every closed point $c$ of $C$. This combines earlier work in (arXiv:0810.2597) with an analysis of weak approximation near boundary points of the parameter spaces for Del Pezzo surfaces of degrees 1 and 2.

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Additional Information

Chenyang Xu
Affiliation: Department of Mathematics, 2-380, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307
Address at time of publication: Beijing International Center of Mathematics Research, 5 Yiheyuan Road, Haidian District, Beijing 100871 China — Department of Mathematics, University of Utah, 155 South 1400 East Salt Lake City, Utah 84112
MR Author ID: 788735
ORCID: 0000-0001-6627-3069

Received by editor(s): January 27, 2010
Received by editor(s) in revised form: December 10, 2010, March 3, 2011, and March 14, 2011
Published electronically: January 18, 2012
Additional Notes: Part of the work was done during the author’s stay at the Institute for Advanced Study, which was supported by the NSF under agreement No. DMS-0635607. The author was partially supported by NSF research grant No. 0969495