The nef cone volume of generalized del pezzo surfaces

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  • Universität Zürich (UZH)
  • Tulane University
  • Southeastern Louisiana University
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OriginalspracheEnglisch
Seiten (von - bis)157-182
Seitenumfang26
FachzeitschriftAlgebra and Number Theory
Jahrgang2
Ausgabenummer2
PublikationsstatusVeröffentlicht - 1 Jan. 2008
Extern publiziertJa

Abstract

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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The nef cone volume of generalized del pezzo surfaces. / Derenthal, Ulrich; Joyce, Michael; Teitler, Zachariah.
in: Algebra and Number Theory, Jahrgang 2, Nr. 2, 01.01.2008, S. 157-182.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Derenthal U, Joyce M, Teitler Z. The nef cone volume of generalized del pezzo surfaces. Algebra and Number Theory. 2008 Jan 1;2(2):157-182. doi: 10.2140/ant.2008.2.157
Derenthal, Ulrich ; Joyce, Michael ; Teitler, Zachariah. / The nef cone volume of generalized del pezzo surfaces. in: Algebra and Number Theory. 2008 ; Jahrgang 2, Nr. 2. S. 157-182.
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