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Mathematische Annalen

, Volume 335, Issue 4, pp 965–989 | Cite as

The pseudo-effective cone of a non-Kählerian surface and applications

  • Andrei Teleman
Article

Abstract

We describe the positive cone and the pseudo-effective cone of a non-Kählerian surface. We use these results for two types of applications:

1. Describe the set Open image in new window of possible total Ricci scalars associated with Gauduchon metrics of fixed volume 1 on a fixed non-Kählerian surface, and decide whether the assignment Open image in new window is a deformation invariant.

2. Study the stability of the canonical extension

Open image in new window

of a class VII surface X with positive b 2. This extension plays an important role in our strategy to prove existence of curves on class VII surfaces, using gauge theoretical methods [Te2].

Our main tools are Buchdahl ampleness criterion for non-Kählerian surfaces [Bu2] and the recent results of Dloussky-Oeljeklaus-Toma [DOT] and Dloussky [D] on class VII surfaces with curves.

Mathematics Subject Classification (2000)

32J15 32Q57 32L05 32G13 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.LATP, CMIUniversité de ProvenceMarseille Cedex 13France

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