Abstract
We prove a vanishing theorem for numerically effective invertible sheaves relative to projective morphisms between irreducible analytic spaces, by using techniques of Kawamata and by introducing intersection numbers on Moišezon spaces. We give applications to Moišezon and strongly pseudoconvex manifolds, extending results of Schneider and T. Peternell.
Keywords
- Global Section
- Normal Crossing
- Coherent Sheaf
- Invertible Sheaf
- Algebraic Space
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Partially supported by C.N.R.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
Ancona, V. Espaces de Moisezon relatifs et algebrisation des modifications analytiques. Math. Ann. 246, 155–165 (1980).
Ancona, V. e Tomassini, G. Modifications analytiques. Lecture Notes on Math. no 943. Berlin, Heidelberg, New York: Springer 1982.
Artin, M. Algebraization of formal moduli, II. Existence of modifications. Ann. of Math., 91, 88–135. (1970).
Deligne, P. Theorie de Hodge II. Publ. Math. IHES 40, 5–58 (1971).
Hartshorne, R. Ample vector bundles. Publ. IHES 29, 63–94 (1966).
Hartshorne, R., Ample subvarieties of algebraic varieties. Lecture Notes in Math. 156. Berlin, Heidelberg, New York: Springer 1970.
Hironaka, H. Flattening theorem in complex analytic geometry. Am. J. of Math. 97, 503–547 (1975).
Kawamata, Y. A generalization of Kodaira — Ramanujam's vanishing theorem. Math. Ann. 261, 43–46 (1982).
Kleiman, S.L. Toward a numerical theory of ampleness. Annals of Math. 84, 293–344 (1966)
Knutson, D. Algebraic spaces. Lecture Notes in Math. no203. Berlin, Heidelberg, New York Springer 1971.
Lieberman, D.-Sernesi, E. Semicontinuity of L-dimension. Math. Ann. 225, 77–88 (1977).
Moišezon, B.G. On n-dimensional compact complex varieties with n algebraically independent meromorphic functions. Amer. Math. Soc. Transl. 63, 51–177 (1967)
Norimatsu, Y. Kodaira vanishing theorem and Chern classes for ¶rt;-manifolds. Proc. Japan Acad. 54, Ser. A, 107–109 (1978).
Peternell, T. On strongly pseudoconvex Kähler manifolds. Inv. Math. 70, 157–168 (1982).
Schneider, M. Some remarks on vanishing theorems for holomorphic vector bundles. Preprint (1983).
Serre, J.P. Géometrie algébrique et géometrie analytique. Ann. Inst. Fourier.
Silva, A. Relative vanishing theorems I: application to ample divisors. Comment. Math. Helvetici 52, 483–489 (1977).
Sommese, A.J. On manifolds that cannot be ample divisors. Math. Ann. 221.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer-Verlag
About this paper
Cite this paper
Ancona, V., Silva, A. (1985). Numerically effective bundles on Moišezon and strongly pseudoconvex manifolds. In: Ławrynowicz, J. (eds) Seminar on Deformations. Lecture Notes in Mathematics, vol 1165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076142
Download citation
DOI: https://doi.org/10.1007/BFb0076142
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16050-2
Online ISBN: 978-3-540-39734-2
eBook Packages: Springer Book Archive
