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
DOI: https://doi.org/10.1090/S1056-3911-2012-00590-6
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
Email: cyxu@math.mit.edu

DOI: https://doi.org/10.1090/S1056-3911-2012-00590-6
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

American Mathematical Society