Numerical characterization of nef arithmetic divisors on arithmetic surfaces

Atsushi Moriwaki

Annales de la faculté des sciences de Toulouse Mathématiques (2014)

  • Volume: 23, Issue: 3, page 717-753
  • ISSN: 0240-2963

Abstract

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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 D ¯ of C 0 -type is nef if and only if D ¯ is pseudo-effective and deg ^ ( D ¯ 2 ) = vol ^ ( D ¯ ) .

How to cite

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Moriwaki, Atsushi. "Numerical characterization of nef arithmetic divisors on arithmetic surfaces." Annales de la faculté des sciences de Toulouse Mathématiques 23.3 (2014): 717-753. <http://eudml.org/doc/275323>.

@article{Moriwaki2014,
abstract = {In this paper, we give a numerical characterization of nef arithmetic $\mathbb\{R\}$-Cartier divisors of $C^0$-type on an arithmetic surface. Namely an arithmetic $\mathbb\{R\}$-Cartier divisor $\overline\{D\}$ of $C^0$-type is nef if and only if $\overline\{D\}$ is pseudo-effective and $\widehat\{\mathrm\{deg\}\}(\overline\{D\}^2) = \widehat\{\mathrm\{vol\}\}(\overline\{D\})$.},
author = {Moriwaki, Atsushi},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Arakelov theory; arithmetic surfaces},
language = {eng},
number = {3},
pages = {717-753},
publisher = {Université Paul Sabatier, Toulouse},
title = {Numerical characterization of nef arithmetic divisors on arithmetic surfaces},
url = {http://eudml.org/doc/275323},
volume = {23},
year = {2014},
}

TY - JOUR
AU - Moriwaki, Atsushi
TI - Numerical characterization of nef arithmetic divisors on arithmetic surfaces
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2014
PB - Université Paul Sabatier, Toulouse
VL - 23
IS - 3
SP - 717
EP - 753
AB - In this paper, we give a numerical characterization of nef arithmetic $\mathbb{R}$-Cartier divisors of $C^0$-type on an arithmetic surface. Namely an arithmetic $\mathbb{R}$-Cartier divisor $\overline{D}$ of $C^0$-type is nef if and only if $\overline{D}$ is pseudo-effective and $\widehat{\mathrm{deg}}(\overline{D}^2) = \widehat{\mathrm{vol}}(\overline{D})$.
LA - eng
KW - Arakelov theory; arithmetic surfaces
UR - http://eudml.org/doc/275323
ER -

References

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