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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc85-0-8,
author = {Andrei Teleman},
title = {Gauge theoretical methods in the classification of non-K\"ahlerian surfaces},
journal = {Banach Center Publications},
volume = {86},
year = {2009},
pages = {109-120},
zbl = {1185.32014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc85-0-8}
}
Andrei Teleman. Gauge theoretical methods in the classification of non-Kählerian surfaces. Banach Center Publications, Tome 86 (2009) pp. 109-120. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc85-0-8/