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

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

2. Study the stability of the canonical extension

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.

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  1. LATP, CMI, Université de Provence, 39 rue F. Joliot-Curie, 13453, Marseille Cedex 13, France

    Andrei Teleman

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  1. Andrei Teleman
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Correspondence to Andrei Teleman.

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Teleman, A. The pseudo-effective cone of a non-Kählerian surface and applications. Math. Ann. 335, 965–989 (2006). https://doi.org/10.1007/s00208-006-0782-3

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  • DOI: https://doi.org/10.1007/s00208-006-0782-3

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