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.
- Ulrich Derenthal
- Affiliation: Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstr. 39, D-80333 München, Germany
- MR Author ID: 776744
- Email: firstname.lastname@example.org
- Andreas-Stephan Elsenhans
- Affiliation: School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Sydney, Australia
- Email: email@example.com
- Jörg Jahnel
- Affiliation: Département Mathematik, Universität Siegen, Walter-Flex-Str. 3, D-57068 Siegen, Germany
- Email: firstname.lastname@example.org
- 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.
- © Copyright 2013 by U. Derenthal, A.-S. Elsenhans, and J. Jahnel
- Journal: Math. Comp. 83 (2014), 965-977
- MSC (2010): Primary 14J26; Secondary 51M20, 14G05
- DOI: https://doi.org/10.1090/S0025-5718-2013-02772-X
- MathSciNet review: 3143700