The pseudo-effective cone of a non-Kählerian surface and applications - Archive ouverte HAL
Article Dans Une Revue Mathematische Annalen Année : 2006

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

Andrei Teleman

Résumé

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 0 - > K_X - > A - > O_X - > 0 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.

Dates et versions

hal-00881267 , version 1 (08-11-2013)

Identifiants

Citer

Andrei Teleman. The pseudo-effective cone of a non-Kählerian surface and applications. Mathematische Annalen, 2006, 335 (4), pp.965-989. ⟨10.1007/s00208-006-0782-3⟩. ⟨hal-00881267⟩
63 Consultations
0 Téléchargements

Altmetric

Partager

More