Numerical character of the effectivity of adjoint line bundles

Campana, Frédéric; Koziarz, Vincent; Păun, Mihai

doi:10.5802/aif.2701

Numerical character of the effectivity of adjoint line bundles
[Le caractère numérique de l’effectivité des systèmes linéaires adjointes]

Campana, Frédéric ¹ ; Koziarz, Vincent ¹ ; Păun, Mihai ¹

¹ Université Henri Poincaré Institut Élie Cartan B.P. 70239 54506 Vandœuvre-lès-Nancy Cedex (France)

Annales de l'Institut Fourier, Tome 62 (2012) no. 1, pp. 107-119.

Résumé
Abstract

Dans cette note nous montrons que le système linéaire adjoint associé à une paire log-canonique est non-vide dés que la classe de Chern de ce système contient un diviseur effectif dont les coefficients sont rationnels. Nous en déduisons quelques corollaires immédiats.

In this note we show that, for any log-canonical pair $(X, Δ)$ , $K_{X} + Δ$ is $ℚ$ -effective if its Chern class contains an effective $ℚ$ -divisor. Then, we derive some direct corollaries.

MR Zbl | 2 citations dans Numdam

DOI : 10.5802/aif.2701

Classification : 14E30
Keywords: Log-canonical pairs, adjoint systems, ramified coverings
Mot clés : paires log-canoniques, systèmes adjoints, recouvrement ramifié

Affiliations des auteurs :

Campana, Frédéric ¹ ; Koziarz, Vincent ¹ ; Păun, Mihai ¹

¹ Université Henri Poincaré Institut Élie Cartan B.P. 70239 54506 Vandœuvre-lès-Nancy Cedex (France)

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     title = {Numerical character of the effectivity of adjoint line bundles},
     journal = {Annales de l'Institut Fourier},
     pages = {107--119},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {62},
     number = {1},
     year = {2012},
     doi = {10.5802/aif.2701},
     zbl = {1250.14009},
     mrnumber = {2986267},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2701/}
}

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Campana, Frédéric; Koziarz, Vincent; Păun, Mihai. Numerical character of the effectivity of adjoint line bundles. Annales de l'Institut Fourier, Tome 62 (2012) no. 1, pp. 107-119. doi : 10.5802/aif.2701. http://www.numdam.org/articles/10.5802/aif.2701/

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