Gauge theoretical methods in the classification of non-Kählerian surfaces

Andrei Teleman (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

The classification of class VII surfaces is a very difficult classical problem in complex geometry. It is considered by experts to be the most important gap in the Enriques-Kodaira classification table for complex surfaces. The standard conjecture concerning this problem states that any minimal class VII surface with b2>0 has b2 curves. By the results of Kato, Nakamura and Dloussky-Oeljeklaus-Toma, this conjecture (if true) would solve the classification problem completely. We explain a new approach (based on techniques from Donaldson theory) to prove existence of curves on class VII surfaces, and we present recent results obtained using this approach.

Mots clés: complex surfaces; class VII surfaces; moduli spaces; instantons; stable bundles

Domaines: Variables complexes [math.CV]; Topologie géométrique [math.GT]; Géométrie différentielle [math.DG]

Andrei Teleman. Gauge theoretical methods in the classification of non-Kählerian surfaces. Algebraic Topology - Old and New, M. M. Postnikov Memorial Conference, Jun 2007, Będlewo, Poland. pp.109-120, ⟨10.4064/bc85-0-8⟩. ⟨hal-00881423⟩