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

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: - Describe the set $\sigma (X)$ of possible total Ricci scalars associated with Gauduchon metrics of fixed volume 1 on a fixed non-Kähhlerian surface, and decide whether the assignment $X\mapsto \sigma (X)$ is a deformation invariant. - Study the stability of the canonical extension $$0\to {\mathcal{K}}_X\to \mathcal{A}\to {\mathcal{O}}_X\to 0$$ of a class VII surface $X$ with positive $b_2$. This extension plays an important role in our strategy to prove the GSS conjecture using gauge theoretical methods.

LaTeX, 25 pages; rv: minor correction in the proof of Remark 4.2

Cited by in corpus (1)

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