Numerical character of the effectivity of adjoint line bundles

[Le caractère numérique de l’effectivité des systèmes linéaires adjointes]

Campana, Frédéric ; Koziarz, Vincent ; Păun, Mihai

Annales de l'Institut Fourier, Tome 62 (2012), p. 107-119 / Harvested from Numdam

Résumé

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.

Abstract

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

Détail

Publié le : 2012-01-01

MR 2986267 | Zbl 1250.14009

DOI : https://doi.org/10.5802/aif.2701
Classification:  14E30
Mots clés: paires log-canoniques, systèmes adjoints, recouvrement ramifié

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