The pseudo-effective cone of a non-Kählerian surface and applications
Abstract
Description
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 $σ(X)$ of possible total Ricci scalars associated with Gauduchon metrics of fixed volume 1 on a fixed non-Kähhlerian surface, and decide whether the assignment $X\mapstoσ(X)$ is a deformation invariant.
- Study the stability of the canonical extension
$$0\to {\cal K}_X\to {\cal A}\to{\cal O}_X\to 0$$ 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
LaTeX, 25 pages; rv: minor correction in the proof of Remark 4.2