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2008 The nef cone volume of generalized Del Pezzo surfaces
Ulrich Derenthal, Michael Joyce, Zachariah Teitler
Algebra Number Theory 2(2): 157-182 (2008). DOI: 10.2140/ant.2008.2.157


We compute a naturally defined measure of the size of the nef cone of a Del Pezzo surface. The resulting number appears in a conjecture of Manin on the asymptotic behavior of the number of rational points of bounded height on the surface. The nef cone volume of a Del Pezzo surface Y with (2)-curves defined over an algebraically closed field is equal to the nef cone volume of a smooth Del Pezzo surface of the same degree divided by the order of the Weyl group of a simply-laced root system associated to the configuration of (2)-curves on Y. When Y is defined over an arbitrary perfect field, a similar result holds, except that the associated root system is no longer necessarily simply-laced.


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Ulrich Derenthal. Michael Joyce. Zachariah Teitler. "The nef cone volume of generalized Del Pezzo surfaces." Algebra Number Theory 2 (2) 157 - 182, 2008.


Received: 27 July 2007; Revised: 19 October 2007; Accepted: 11 December 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1158.14032
MathSciNet: MR2377367
Digital Object Identifier: 10.2140/ant.2008.2.157

Primary: 14J26
Secondary: 14C20, 14G05

Rights: Copyright © 2008 Mathematical Sciences Publishers


Vol.2 • No. 2 • 2008
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