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Numerical characterization of nef arithmetic divisors on arithmetic surfaces
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 23 (2014) no. 3, pp. 717-753.

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

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

@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, Toulouse},
     volume = {Ser. 6, 23},
     number = {3},
     year = {2014},
     doi = {10.5802/afst.1422},
     zbl = {06374886},
     mrnumber = {3266711},
     language = {en},
     url = {afst.centre-mersenne.org/item/AFST_2014_6_23_3_717_0/}
}
Atsushi Moriwaki. Numerical characterization of nef arithmetic divisors on arithmetic surfaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 23 (2014) no. 3, pp. 717-753. doi : 10.5802/afst.1422. https://afst.centre-mersenne.org/item/AFST_2014_6_23_3_717_0/

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