Numerical character of the effectivity of adjoint line bundles
Annales de l'Institut Fourier, Volume 62 (2012) no. 1, pp. 107-119.

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

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.

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, Volume 62 (2012) no. 1, pp. 107-119. doi : 10.5802/aif.2701. http://www.numdam.org/articles/10.5802/aif.2701/

[1] Arapura, Donu Higgs line bundles, Green-Lazarsfeld sets, and maps of Kähler manifolds to curves, Bull. Amer. Math. Soc., Volume 26 (1992) no. 2, pp. 310-314 | DOI | MR | Zbl

[2] Arapura, Donu Geometry of cohomology support loci for local systems. I, J. Algebraic Geom., Volume 6 (1997) no. 3, pp. 563-597 | MR | Zbl

[3] Birkar, Caucher; Cascini, Paolo; Hacon, Christopher D.; McKernan, James Existence of minimal models for varieties of log general type, J. Amer. Math. Soc., Volume 23 (2010) no. 2, pp. 405-468 | DOI | MR

[4] Budur, Nero Unitary local systems, multiplier ideals, and polynomial periodicity of Hodge numbers, Adv. Math., Volume 221 (2009) no. 1, pp. 217-250 | DOI | MR

[5] Campana, F.; Peternell, T.; Toma, M. Geometric stability of the cotangent bundle and the universal cover of a projective manifold (arXiv:math/0405093, to appear in Bull. Soc. Math. France) | Numdam | MR

[6] Chen, J.; Hacon, C. On the irregularity of the image of the Iitaka fibration, Comm. in Algebra, Volume 32 (2004) no. 1, pp. 203-215 | DOI | MR

[7] Esnault, Hélène; Viehweg, Eckart Logarithmic de Rham complexes and vanishing theorems, Invent. Math., Volume 86 (1986) no. 1, pp. 161-194 | DOI | MR | Zbl

[8] Fujino, O. On Kawamata’s theorem (arXiv:0910.1156)

[9] Fukuda, S. An elementary semi-ampleness result for log-canonical divisors (arXiv:1003,1388)

[10] Gongyo, Y. Abundance theorem for numerically trivial log canonical divisors of semi-log canonical pairs (arXiv:1005.2796)

[11] Kawamata, Y. On the abundance theorem in the case ν=0 (arXiv:1002.2682)

[12] Kawamata, Y. Pluricanonical systems on minimal algebraic varieties, Invent. Math., Volume 79 (1985) no. 3, pp. 567-588 | DOI | MR | Zbl

[13] Kollár, János; Mori, Shigefumi Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, 134, Cambridge University Press, Cambridge, 1998 (With the collaboration of C. H. Clemens and A. Corti, Translated from the 1998 Japanese original) | DOI | MR | Zbl

[14] Nakayama, Noboru Zariski-decomposition and abundance, MSJ Memoirs, 14, Mathematical Society of Japan, Tokyo, 2004 | MR

[15] Păun, M Relative critical exponents, non-vanishing and metrics with minimal singularities (arXiv:0807.3109)

[16] Shokurov, V. V. A nonvanishing theorem, Izv. Akad. Nauk SSSR Ser. Mat., Volume 49 (1985) no. 3, pp. 635-651 | MR | Zbl

[17] Simpson, C. Subspaces of moduli spaces of rank one local systems, Ann. Sci. E.N.S. (4), Volume 26 (1993) no. 3, pp. 361-401 | Numdam | MR | Zbl

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