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Counting integral points on universal torsors


Derenthal, U (2009). Counting integral points on universal torsors. International Mathematics Research Notices, 2009(14):2648-2699.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > General Mathematics
Language:English
Date:2009
Deposited On:14 Jan 2010 13:59
Last Modified:23 Jan 2022 15:08
Publisher:Oxford University Press
ISSN:1073-7928
OA Status:Green
Publisher DOI:https://doi.org/10.1093/imrn/rnp030
  • Content: Published Version
  • Language: English
  • Description: Nationallizenz 142-005