Details
| Original language | English |
|---|---|
| Pages (from-to) | 2648-2699 |
| Number of pages | 52 |
| Journal | International Mathematics Research Notices |
| Volume | 2009 |
| Issue number | 14 |
| Publication status | Published - 1 Dec 2009 |
| Externally published | Yes |
Abstract
Manin's conjecture for the asymptotic behavior of the number of rational points of bounded height on del Pezzo surfaces can be approached through universal torsors. We prove several auxiliary results for the estimation of the number of integral points in certain regions on universal torsors. As an application, we prove Manin's conjecture for a singular quartic del Pezzo surface.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: International Mathematics Research Notices, Vol. 2009, No. 14, 01.12.2009, p. 2648-2699.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Counting integral points on universal torsors
AU - Derenthal, Ulrich
N1 - Funding information: U.D. was partially supported by a Feodor Lynen Research Fellowship of the Alexander von Humboldt Foundation and grant 1646/1-1 of the Deutsche Forschungsgemeinschaft.
PY - 2009/12/1
Y1 - 2009/12/1
N2 - Manin's conjecture for the asymptotic behavior of the number of rational points of bounded height on del Pezzo surfaces can be approached through universal torsors. We prove several auxiliary results for the estimation of the number of integral points in certain regions on universal torsors. As an application, we prove Manin's conjecture for a singular quartic del Pezzo surface.
AB - Manin's conjecture for the asymptotic behavior of the number of rational points of bounded height on del Pezzo surfaces can be approached through universal torsors. We prove several auxiliary results for the estimation of the number of integral points in certain regions on universal torsors. As an application, we prove Manin's conjecture for a singular quartic del Pezzo surface.
UR - http://www.scopus.com/inward/record.url?scp=78650036873&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnp030
DO - 10.1093/imrn/rnp030
M3 - Article
AN - SCOPUS:78650036873
VL - 2009
SP - 2648
EP - 2699
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - 14
ER -