The pseudo-effective cone of a non-K\"ahlerian surface and applications

We describe the positive cone and the pseudo-effective cone of a non-K"ahlerian 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-K"ahhlerian surface, and decide whether the assignment $X \mapsto σ (X)$ is a deformation invariant.
Study the stability of the canonical extension $0 \to K_{X} \to A \to O_{X} \to 0$ 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.

We describe the positive cone and the pseudo-effective cone of a non-K"ahlerian 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-K"ahhlerian surface, and decide whether the assignment $X \mapsto σ (X)$ is a deformation invariant.
Study the stability of the canonical extension $0 \to K_{X} \to A \to O_{X} \to 0$ 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.

文献摘要