Class VII-surfaces

Class VII surfaces

Andrej Teleman uses gauge theoretical methods to prove existence on curves of class VII surfaces with b₂=1, 2. See [T1], [T2].
It is known that the existence of a cycle of rational curves was the missing ingredient permitting to classify surfaces of class VII with b₂>0 completely. This classification makes use of another important reduction step: existence of a global spherical shell reduces to the existence of 'sufficiently many curves.
A major recent contribution can be found in [D-O-T]
These recent contributions form a major step forward in the classification of class VII-surfaces.

[T1] Teleman, A.: Donaldson theory on non-Kählerian surfaces and class VII surfaces with
b₂ = 1, Invent. math. 162, 493-521 (2005)

[T2] Teleman, A.: Instantons and curves on class VII surfaces http://fr.arxiv.org/abs/0704.2634

[D-O-T] Georges Dloussky, Karl Oeljeklaus, Matei Toma: Class VII surfaces with b₂ curves, http://fr.arxiv.org/abs/math/0201010