On compact Kähler surfaces

Nicholas Buchdahl

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 1, page 287-302
  • ISSN: 0373-0956

Abstract

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Without relying on the classification of compact complex surfaces, it is proved that every such surface with even first Betti number admits a Kähler metric and that a real form of the classical Nakai-Moishezon criterion holds on the surface.

How to cite

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Buchdahl, Nicholas. "On compact Kähler surfaces." Annales de l'institut Fourier 49.1 (1999): 287-302. <http://eudml.org/doc/75337>.

@article{Buchdahl1999,
abstract = {Without relying on the classification of compact complex surfaces, it is proved that every such surface with even first Betti number admits a Kähler metric and that a real form of the classical Nakai-Moishezon criterion holds on the surface.},
author = {Buchdahl, Nicholas},
journal = {Annales de l'institut Fourier},
keywords = {compact complex surfaces; Kähler metric; Nakai criterion; positive current},
language = {eng},
number = {1},
pages = {287-302},
publisher = {Association des Annales de l'Institut Fourier},
title = {On compact Kähler surfaces},
url = {http://eudml.org/doc/75337},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Buchdahl, Nicholas
TI - On compact Kähler surfaces
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 1
SP - 287
EP - 302
AB - Without relying on the classification of compact complex surfaces, it is proved that every such surface with even first Betti number admits a Kähler metric and that a real form of the classical Nakai-Moishezon criterion holds on the surface.
LA - eng
KW - compact complex surfaces; Kähler metric; Nakai criterion; positive current
UR - http://eudml.org/doc/75337
ER -

References

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  1. [BPV] W. BARTH, C. PETERS and A. VAN de VEN, Compact Complex Surfaces, Berlin-Heidelberg-New York, Springer, 1984. Zbl0718.14023MR86c:32026
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  3. [D1] J.-P. DEMAILLY, Regularization of closed positive currents and intersection theory, J. Alg. Geom., 1 (1992), 361-409. Zbl0777.32016MR93e:32015
  4. [D2] J.-P. DEMAILLY, Regularization of closed positive currents of type (1,1) by the flow of a Chern connection, in: Contributions to complex analysis and analytic geometry: dedicated to Pierre Dolbeault, ed. H. Skoda and J. M. Trépreau, Wiesbaden, Vieweg 1994. Zbl0824.53064
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  6. [GT] D. GILBARG and N. TRUDINGER, Elliptic partial differential equations of second order, 2nd ed. Berlin-Heidelberg-New York, Springer, 1983. Zbl0562.35001MR86c:35035
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  8. [HL] R. HARVEY and H. B. LAWSON, An intrinsic characterisation of Kähler manifolds, Invent. Math., 74 (1983), 169-198. Zbl0553.32008MR85b:32013
  9. [MK] J. MORROW and K. KODAIRA, Complex Manifolds, Holt-Rinehart & Wilson, New York, 1971. Zbl0325.32001MR46 #2080
  10. [M] Y. MIYAOKA, Kähler metrics on elliptic surfaces, Proc. Japan Acad., 50 (1974), 533-536. Zbl0354.32011MR57 #723
  11. [S1] Y.-T. SIU, Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math., 27 (1974), 53-156. Zbl0289.32003MR50 #5003
  12. [S2] Y.-T. SIU, Review of [T] in Mathematical Reviews, (1982) MR#82k:32065. 
  13. [S3] Y.-T. SIU, Every K3 surface is Kähler, Invent. Math., 73 (1983), 139-150. Zbl0557.32004MR84j:32036
  14. [T] A. N. TODOROV, Applications of the Kähler-Einstein-Calabi-Yau metric to moduli of K3 surfaces, Invent. Math., 61 (1980), 251-265. Zbl0472.14006MR82k:32065
  15. [Y] S.-T. YAU, On the Ricci curvature of a complex Kähler manifold and the complex Monge-Ampère equation, Comm. Pure Appl. Math., 31 (1978), 339-411. Zbl0369.53059MR81d:53045

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