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Mathematische Zeitschrift

, Volume 238, Issue 3, pp 555–568 | Cite as

Bihermitian surfaces with odd first Betti number

  • Vestislav Apostolov

Abstract.

Compact bihermitian surfaces are considered, that is, compact, oriented, conformal four-manifolds admitting two distinct compatible complex structures. It is shown that if the first Betti number is odd then, with respect to either complex structure, such a manifold belongs to Class VII of the Enriques-Kodaira classification. Moreover, it must be either a special Hopf or an Inoue surface (in the strongly bihermitian case), or obtained by blowing-up a minimal class VII surface with curves (in the non-strongly bihermitian case).

Keywords

Betti Number Compatible Complex Minimal Class Compatible Complex Structure Inoue Surface 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Vestislav Apostolov
    • 1
  1. 1.Department of Mathematics, UQAM, C.P. 8888, succ. Centre-ville, Montreal (Quebec) H3C 3P8, Canada (e-mail: apostolo@math.uqam.ca)CA

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