Numerical character of the effectivity of adjoint line bundles

Frédéric Campana[1]; Vincent Koziarz[1]; Mihai Păun[1]

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

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 1, page 107-119
  • ISSN: 0373-0956

Abstract

top
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.

How to cite

top

Campana, Frédéric, Koziarz, Vincent, and Păun, Mihai. "Numerical character of the effectivity of adjoint line bundles." Annales de l’institut Fourier 62.1 (2012): 107-119. <http://eudml.org/doc/251075>.

@article{Campana2012,
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.},
affiliation = {Université Henri Poincaré Institut Élie Cartan B.P. 70239 54506 Vandœuvre-lès-Nancy Cedex (France); Université Henri Poincaré Institut Élie Cartan B.P. 70239 54506 Vandœuvre-lès-Nancy Cedex (France); Université Henri Poincaré Institut Élie Cartan B.P. 70239 54506 Vandœuvre-lès-Nancy Cedex (France)},
author = {Campana, Frédéric, Koziarz, Vincent, Păun, Mihai},
journal = {Annales de l’institut Fourier},
keywords = {Log-canonical pairs; adjoint systems; ramified coverings; log canonical pairs},
language = {eng},
number = {1},
pages = {107-119},
publisher = {Association des Annales de l’institut Fourier},
title = {Numerical character of the effectivity of adjoint line bundles},
url = {http://eudml.org/doc/251075},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Campana, Frédéric
AU - Koziarz, Vincent
AU - Păun, Mihai
TI - Numerical character of the effectivity of adjoint line bundles
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 1
SP - 107
EP - 119
AB - 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.
LA - eng
KW - Log-canonical pairs; adjoint systems; ramified coverings; log canonical pairs
UR - http://eudml.org/doc/251075
ER -

References

top
  1. Donu Arapura, Higgs line bundles, Green-Lazarsfeld sets, and maps of Kähler manifolds to curves, Bull. Amer. Math. Soc. 26 (1992), 310-314 Zbl0759.14016MR1129312
  2. Donu Arapura, Geometry of cohomology support loci for local systems. I, J. Algebraic Geom. 6 (1997), 563-597 Zbl0923.14010MR1487227
  3. Caucher Birkar, Paolo Cascini, Christopher D. Hacon, James McKernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010), 405-468 Zbl1210.14019MR2601039
  4. Nero Budur, Unitary local systems, multiplier ideals, and polynomial periodicity of Hodge numbers, Adv. Math. 221 (2009), 217-250 Zbl1187.14024MR2509325
  5. F. Campana, T. Peternell, M. Toma, Geometric stability of the cotangent bundle and the universal cover of a projective manifold Zbl1218.14030MR2815027
  6. J. Chen, C. Hacon, On the irregularity of the image of the Iitaka fibration, Comm. in Algebra 32 (2004), 203-215 Zbl1137.14008MR2036231
  7. Hélène Esnault, Eckart Viehweg, Logarithmic de Rham complexes and vanishing theorems, Invent. Math. 86 (1986), 161-194 Zbl0603.32006MR853449
  8. O. Fujino, On Kawamata’s theorem Zbl1213.14015
  9. S. Fukuda, An elementary semi-ampleness result for log-canonical divisors Zbl1258.14019
  10. Y. Gongyo, Abundance theorem for numerically trivial log canonical divisors of semi-log canonical pairs Zbl1312.14024
  11. Y. Kawamata, On the abundance theorem in the case ν = 0  Zbl1263.14017
  12. Y. Kawamata, Pluricanonical systems on minimal algebraic varieties, Invent. Math. 79 (1985), 567-588 Zbl0593.14010MR782236
  13. János Kollár, Shigefumi Mori, Birational geometry of algebraic varieties, 134 (1998), Cambridge University Press, Cambridge Zbl0926.14003MR1658959
  14. Noboru Nakayama, Zariski-decomposition and abundance, 14 (2004), Mathematical Society of Japan, Tokyo Zbl1061.14018MR2104208
  15. M Păun, Relative critical exponents, non-vanishing and metrics with minimal singularities Zbl1251.32018
  16. V. V. Shokurov, A nonvanishing theorem, Izv. Akad. Nauk SSSR Ser. Mat. 49 (1985), 635-651 Zbl0605.14006MR794958
  17. C. Simpson, Subspaces of moduli spaces of rank one local systems, Ann. Sci. E.N.S. (4) 26 (1993), 361-401 Zbl0798.14005MR1222278

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.