no. 1
Numerical character of the effectivity of adjoint line bundles
[Le caractère numérique de l’effectivité des systèmes linéaires adjointes]
Campana, Frédéric1 ; Koziarz, Vincent1 ; Păun, Mihai1
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.

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.

DOI : 10.5802/aif.2701
Classification : 14E30
Keywords: Log-canonical pairs, adjoint systems, ramified coverings
Mot clés : paires log-canoniques, systèmes adjoints, recouvrement ramifié

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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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. https://aif.centre-mersenne.org/articles/10.5802/aif.2701/

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