Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-24T09:15:38.503Z Has data issue: false hasContentIssue false
  • English
  • Français

An injectivity theorem

Part of: Birational geometry (Co)homology theory

Published online by Cambridge University Press:  12 May 2014

Florin Ambro
Florin Ambro*
Affiliation:
Institute of Mathematics ‘Simion Stoilow’ of the Romanian Academy, PO box 1-764, RO-014700 Bucharest, Romania email florin.ambro@imar.ro
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We generalize the injectivity theorem of Esnault and Viehweg, and apply it to the structure of log canonical type divisors.

Keywords

logarithmic differential formslog varietiestotally canonical locusnon-log canonical locus

MSC classification

Secondary: 14F17: Vanishing theorems 14E30: Minimal model program (Mori theory, extremal rays)
Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 6 , June 2014 , pp. 999 - 1023
Copyright
© The Author 2014 

References

Ambro, F., Quasi-log varieties, in Birational geometry: linear systems and finitely generated algebras: collected papers, Proceedings of the Steklov Institute of Mathematics, vol. 240, eds Iskovskikh, V. A. and Shokurov, V. V. (Nauka, Moscow, 2003), 220–239.Google Scholar
Ambro, F., Basic properties of log canonical centers. Preprint (2006), arXiv:math/0611205.Google Scholar
Ambro, F., Cyclic covers and toroidal embeddings. Preprint (2013), arXiv:1310.3951.Google Scholar
Atiyah, M. F and Hodge, W. V. D, Integrals of the second kind on an algebraic variety, Ann. of Math. (2) 62 (1955), 56–91.Google Scholar
Deligne, P., Théorème de Lefschetz et critères de dégénérescence de suites spectrales, Publ. Math. Inst. Hautes Études Sci. 35 (1969), 107–126.Google Scholar
Deligne, P., Equations differentielles a points singulieres regulieres, Lecture Notes in Mathematics, vol. 163 (Springer, Heidelberg, 1970).Google Scholar
Deligne, P., Théorie de Hodge II, Publ. Math. Inst. Hautes Études Sci. 40 (1971), 5–57.Google Scholar
Deligne, P., Théorie de Hodge III, Publ. Math. Inst. Hautes Études Sci. 44 (1974), 5–77.Google Scholar
Du Bois, P., Complexe de de Rham filtré d’une variété singuliére, Bull. Soc. Math. France 109 (1981), 41–81.Google Scholar
Du Bois, P. and Jarraud, P., Une propriété de commutation au changement de base des images directes supérieures de faisceaux structural, C. R. Acad. Sci. Paris, Sér. A 279 (1974), 745–747.Google Scholar
Esnault, H. and Viehweg, E., Revêtements cycliques, in Algebraic threefolds (Varenna, 1981), Lecture Notes in Mathematics, vol. 947 (Springer, Berlin–New York, 1982), 241–250.Google Scholar
Esnault, H. and Viehweg, E., Logarithmic de Rham complexes and vanishing theorems, Invent. Math. 86 (1986), 161–194.Google Scholar
Esnault, H. and Viehweg, E., Lectures on vanishing theorems, in DMV Seminar (Birkhaüser, Basel, 1992).Google Scholar
Grothendieck, A., Eléments de géométrie algébrique (rédigés avec la collaboration de Jean Dieudonné): III. Étude cohomologique des faisceaux coherents, Premiére partie, Publ. Math. Inst. Hautes Études Sci. 11 (1961), 5–167.Google Scholar
Grothendieck, A., On the de Rham cohomology of algebraic varieties, Publ. Math. Inst. Hautes Études Sci. 29 (1966), 95–103.Google Scholar
Kawamata, Y., A generalization of Kodaira–Ramanujam’s vanishing theorem, Math. Ann. 261 (1982), 43–46.CrossRefGoogle Scholar
Kodaira, K., On a differential-geometric method in the theory of analytic stacks, Proc. Natl. Acad. Sci. USA 39 (1953), 1268–1273.CrossRefGoogle ScholarPubMed
Kollár, J., Higher direct images of dualizing sheaves I, Ann. of Math. (2) 123 (1986), 11–42.Google Scholar
Miyaoka, Y., On the Mumford–Ramanujam vanishing theorem on a surface, in Proceedings of Géometrie Algébrique d’Angers, July 1979 (Sijthoff & Noordhoff, Alphen aan den Rijn Germantown, MD, 1980), 239–247.Google Scholar
Mumford, D., Pathologies III, Amer. J. Math. 89 (1967), 94–104.Google Scholar
Ramanujam, C. P., Remarks on the Kodaira vanishing theorem, J. Indian Math. Soc. (N.S.) (1972), 41–51.Google Scholar
Ramanujam, C. P., Supplement to the article [Ram72], J. Indian Math. Soc. (N.S.) 38 (1974), 121–124.Google Scholar
Raynaud, M., Contre-exemple au vanishing theorem en caractéristique p > 0, in C. P. Ramanujam—A tribute, Studies in Mathematics, vol. 8 (Tata Institute of Fundamental Research, Bombay, 1978), 273–278.Google Scholar
Serre, J.-P., Faisceaux algebriques coherents, Ann. of Math. (2) 61 (1955), 197–278.Google Scholar
Shokurov, V. V., Three-dimensional log perestroikas, Russian Acad. Sci. Izv. Math. 40 (1993), 95–202.Google Scholar
Shokurov, V. V., Prelimiting flips, in Birational geometry: linear systems and finitely generated algebras: collected papers, Proceedings of the Steklov Institute of Mathematics, vol. 240, eds Iskovskikh, V. A. and Shokurov, V. V. (Nauka, Moscow, 2003), 75–213.Google Scholar
Tankeev, S. G., On n-dimensional canonically polarized varieties and varieties of fundamental type, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 31–44.Google Scholar
Viehweg, E., Vanishing theorems, J. Reine Angew. Math. 335 (1982), 1–8.Google Scholar
Zariski, O., Algebraic surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 3 (Springer, 1935).Google Scholar