Positivity on subvarieties and vanishing of higher cohomology

Alex Küronya[1]

  • [1] Budapest University of Technology and Economics, Department of Algebra, P.O. Box 91, H-1521 Budapest, Hungary Albert-Ludwigs-Universität Freiburg, Mathematisches Institut, Eckerstraße 1, D-79104 Freiburg, Germany

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 5, page 1717-1737
  • ISSN: 0373-0956

Abstract

top
We study the relationship between positivity of restriction of line bundles to general complete intersections and vanishing of their higher cohomology. As a result, we extend classical vanishing theorems of Kawamata–Viehweg and Fujita to possibly non-nef divisors.

How to cite

top

Küronya, Alex. "Positivity on subvarieties and vanishing of higher cohomology." Annales de l’institut Fourier 63.5 (2013): 1717-1737. <http://eudml.org/doc/275516>.

@article{Küronya2013,
abstract = {We study the relationship between positivity of restriction of line bundles to general complete intersections and vanishing of their higher cohomology. As a result, we extend classical vanishing theorems of Kawamata–Viehweg and Fujita to possibly non-nef divisors.},
affiliation = {Budapest University of Technology and Economics, Department of Algebra, P.O. Box 91, H-1521 Budapest, Hungary Albert-Ludwigs-Universität Freiburg, Mathematisches Institut, Eckerstraße 1, D-79104 Freiburg, Germany},
author = {Küronya, Alex},
journal = {Annales de l’institut Fourier},
keywords = {vanishing theorems; generic restrictions of line bundles; q-ampleness; vanishing of higher cohomology; partial positivity},
language = {eng},
number = {5},
pages = {1717-1737},
publisher = {Association des Annales de l’institut Fourier},
title = {Positivity on subvarieties and vanishing of higher cohomology},
url = {http://eudml.org/doc/275516},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Küronya, Alex
TI - Positivity on subvarieties and vanishing of higher cohomology
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 5
SP - 1717
EP - 1737
AB - We study the relationship between positivity of restriction of line bundles to general complete intersections and vanishing of their higher cohomology. As a result, we extend classical vanishing theorems of Kawamata–Viehweg and Fujita to possibly non-nef divisors.
LA - eng
KW - vanishing theorems; generic restrictions of line bundles; q-ampleness; vanishing of higher cohomology; partial positivity
UR - http://eudml.org/doc/275516
ER -

References

top
  1. Aldo Andreotti, Hans Grauert, Théorèmes de finitude por la cohomologie des espaces complexes, Bull. Soc. Math. France 90 (1962), 193-259 Zbl0106.05501MR150342
  2. Sébastien Boucksom, Jean-Pierre Demailly, Mihai Păun, Thomas Peternell, The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension Zbl1267.32017
  3. Jean-Pierre Demailly, Holomorphic Morse inequalities and asymptotic cohomology groups: a tribute to Bernhard Riemann, Milan Journal of Mathematics 78 (2010), 265-277 Zbl1205.32017MR2684780
  4. Jean-Pierre Demailly, Thomas Peternell, Michael Schneider, Holomorphic line bundles with partially vanishing cohomology, Proceedings of the Hirzebruch 65 conference on algebraic geometry (Ramat Gan, 1993) (1996), 165-198, Bar-Ilan University Zbl0859.14005MR1360502
  5. Lawrence Ein, Robert Lazarsfeld, Mircea Mustaţă, Michael Nakamaye, Mihnea Popa, Asymptotic invariants of line bundles, Pure Appl. Math. Q. 1 (2005), 379-403 Zbl1139.14008MR2194730
  6. Lawrence Ein, Robert Lazarsfeld, Mircea Mustaţă, Michael Nakamaye, Mihnea Popa, Asymptotic invariants of base loci, Ann. Inst. Fourier (Grenoble) 56 (2006), 1701-1734 Zbl1127.14010MR2282673
  7. Tommaso de Fernex, Alex Küronya, Robert Lazarsfeld, Higher cohomology of divisors on projective varieties, Mathematische Annalen 337 (2007), 443-455 Zbl1127.14012MR2262793
  8. Takao Fujita, Vanishing theorems for semipositive line bundles, Algebraic geometry (Tokyo/Kyoto, 1982) 1016 (1983), 519-528, Springer, Berlin Zbl0522.14010MR726440
  9. Robin Hartshorne, Algebraic geometry, (1977), Springer Verlag, Berlin Zbl0531.14001MR463157
  10. Alex Küronya, Asymptotic cohomological functions on projective varieties, American Journal of Mathematics 128 (2006), 1475-1519 Zbl1114.14005MR2275909
  11. Robert Lazarsfeld, Positivity in Algebraic Geometry I.-II, 48-49 (2004), 519-528, Springer Verlag, Berlin Zbl1093.14500MR2095471
  12. Shin-ichi Matsumura, Restricted volumes and divisorial Zariski decompositions Zbl1277.14006
  13. Sebastian Neumann, A decomposition of the moving cone of a projective manifold according to the Harder-Narasimhan filtration of the tangent bundle, (2009) Zbl1196.14004
  14. Burt Totaro, Line bundles with partially vanishing cohomology Zbl1277.14007

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.