Numerical characterization of nef arithmetic divisors on arithmetic surfaces

Atsushi Moriwaki

doi:10.5802/afst.1422

Atsushi Moriwaki

Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 23 (2014) no. 3, pp. 717-753.

Abstract
Abstract

In this paper, we give a numerical characterization of nef arithmetic $ℝ$ -Cartier divisors of $C^{0}$ -type on an arithmetic surface. Namely an arithmetic $ℝ$ -Cartier divisor $\bar{D}$ of $C^{0}$ -type is nef if and only if $\bar{D}$ is pseudo-effective and $\hat{\deg} ({\bar{D}}^{2}) = \hat{vol} (\bar{D})$ .

Dans le présent article, nous donnons une caractérisation numérique des $ℝ$ -diviseurs arithmétiques nef et de type $C^{0}$ sur une surface artihmétique. Plus exactement, nous montrons qu’un $ℝ$ -diviseur de Cartier $\bar{D}$ de type $C^{0}$ est nef si et seulement si $\bar{D}$ est pseudo-effectif et $\hat{\deg} ({\bar{D}}^{2}) = \hat{vol} (\bar{D})$ .

MR Zbl

DOI: 10.5802/afst.1422

@article{AFST_2014_6_23_3_717_0,
     author = {Atsushi Moriwaki},
     title = {Numerical characterization of nef arithmetic divisors on arithmetic surfaces},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {717--753},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 23},
     number = {3},
     year = {2014},
     doi = {10.5802/afst.1422},
     mrnumber = {3266711},
     zbl = {06374886},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1422/}
}

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Atsushi Moriwaki. Numerical characterization of nef arithmetic divisors on arithmetic surfaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 23 (2014) no. 3, pp. 717-753. doi : 10.5802/afst.1422. https://afst.centre-mersenne.org/articles/10.5802/afst.1422/

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