Gauge theoretical methods in the classification of non-Kählerian surfaces

• Autorzy: Andrei Teleman
• Języki publikacji: EN

Abstrakty

EN

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 [Ka1]-[Ka3], [Na1]-[Na3], [DOT], [OT] 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.

Kategorie tematyczne

• 32Q55: Topological aspects of complex manifolds
• 53C07: Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
• 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants
• 32Q57: Classification theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2009
• Tom: 85
• Numer: 1
• Strony: 109-120

Daty

wydano

2009

Twórcy

autor

Andrei Teleman

• LATP, CMI, Université de Provence, 39 Rue Frédéric Joliot-Curie, 13453 Marseille, France

Identyfikatory

DOI

10.4064/bc85-0-8