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On the factor alpha in Peyre’s constant

Authors: Ulrich Derenthal, Andreas-Stephan Elsenhans and Jörg Jahnel
Journal: Math. Comp. 83 (2014), 965-977
MSC (2010): Primary 14J26; Secondary 51M20, 14G05
Published electronically: September 17, 2013
MathSciNet review: 3143700
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Abstract: For an arbitrary del Pezzo surface $S$, we compute $\alpha (S)$, which is the volume of a certain polytope in the dual of the effective cone of $S$, using magma and polymake. The constant $\alpha (S)$ appears in Peyre’s conjecture for the asymptotic formula for the number of rational points of bounded height on $S$ over number fields.

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Additional Information

Ulrich Derenthal
Affiliation: Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstr. 39, D-80333 München, Germany
MR Author ID: 776744

Andreas-Stephan Elsenhans
Affiliation: School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Sydney, Australia

Jörg Jahnel
Affiliation: Département Mathematik, Universität Siegen, Walter-Flex-Str. 3, D-57068 Siegen, Germany

Keywords: Peyre’s constant, del Pezzo surface, polyhedron, volume, polymake
Received by editor(s): February 28, 2012
Published electronically: September 17, 2013
Additional Notes: The first author was partly supported by Deutsche Forschungsgemeinschaft (DFG) grant DE 1646/2-1, SNF grant 200021_124737/1, and by the Center for Advanced Studies of LMU München.
The second author was supported in part by the Deutsche Forschungsgemeinschaft (DFG) through a funded research project.
Article copyright: © Copyright 2013 by U. Derenthal, A.-S. Elsenhans, and J. Jahnel