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
Full-text PDF
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.
References
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References
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- Hassett, B.; Tschinkel, Y.; Weak approximation over function fields. Invent. Math. 163 (2006), no. 1, 171–190. MR 2208420 (2007b:14109)
- Hassett, B.; Tschinkel, Y.; Approximation at places of bad reduction for rationally connected varieties, Pure and Applied Mathematics Quarterly 4 (2008) no. 3, 743-766. MR 2435843 (2010h:14081)
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- Voisin, C.; Hodge theory and complex algebraic geometry. II. Translated from the French by Leila Schneps. Cambridge Studies in Advanced Mathematics 77, Cambridge University Press, Cambridge, 2003. MR 1997577 (2005c:32024b)
- Xu. C.; Strong rational connectedness of surfaces, arXiv:0810.2597 in J. Reine Angew. Math. (to appear).
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
Email:
cyxu@math.mit.edu
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
