Gauge theoretical methods in the classification of non-Kaehlerian surfaces

2008/04/03 by Andrei Teleman, Teleman, Andrei
Mathematics · #32Q55 #32Q57 #53C07 #57R57 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Geometric Topology (math.GT) #math.AG #math.CV #math.GT #msc:32Q55 #msc:32Q57 #msc:53C07 #msc:57R57

paper · pdf · doi:10.48550/arxiv.0804.0557

12 pages, 2 figures, talk given at the Postnikov Memorial Conference, Bedlewo (Poland) June 2007, to appear in Banach Center Publications

arxiv created 2008/04/03 · arxiv updated 2009/12/01

Abstract

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 this 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.

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