Abstract
We study the class of compact complex manifolds which are proper modifications of compact Kähler manifolds. It is shown, by means of new results about positive \(\partial \bar \partial \)-closed currents, that they carry a balanced metric. The notion of p-Kähler manifold is introduced in order to attempt a classification of these modifications.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. Alessandrini & M. Andreatta, Closed transverse (p,p)-forms on compact complex manifolds, Compositio Math. 61 (1987) 181–200. Erratum ibidem 63 (1987) 143.
L. Alessandrini & G. Bassanelli, Compact p-Kähler manifolds, to appear on Geometriae Dedicata.
L. Alessandrini & G. Bassanelli, A balanced proper modification of P 3, to appear.
L. Alessandrini & G. Bassanelli, Positive ∂∂̄-closed currents and non Kähler geometry, to appear.
A. Borel & A. Haefliger, La classe d’homologie fondamentale d’un espace analytique, Bull. Soc. Math. France 89 (1961) 461–513.
A. Blanchard, Sur les variétés analytiques complexes, Ann. Sc. Ecole Norm. Sup. 73 (1956) 157–202.
P. Gauduchon, Fibres hermitiens a endomorphisme de Ricci non négatif, Bull. Soc. Math. France 105 (1977) 113–140.
H. Grauert & R. Remmert, Coherent Analytic Sheaves, Springer Verlag, Berlin 1984.
H. Grauert & O. Riemenschneider, Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen, Inv. Math. 11 (1970) 263–292.
H. Hironaka, Flattening theorems in complex analytic geometry, Amer. J. Math. 97 (1975) 503–547.
R. Harvey & J.R. Lawson, An intrinsec characterization of Kähler manifolds, Inv. Math. 74 (1983) 169–198.
M.L. Michelson, On the existence of special metrics in complex geometry, Acta Math. 143 (1983) 261–295.
J. Varouchas, Kähler Spaces and Proper Open Morphisms, Math. Ann. 283 (1989) 13–52. Dipartimento di Matematica Università di Trento I-38050 POVO (Trento) (Italy).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
About this paper
Cite this paper
Alessandrini, L., Bassanelli, G. (1991). Smooth proper modifications of compact Kähler manifolds. In: Diederich, K. (eds) Complex Analysis. Aspects of Mathematics, vol 1. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-86856-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-322-86856-5_1
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-322-86858-9
Online ISBN: 978-3-322-86856-5
eBook Packages: Springer Book Archive