Gauge theoretical methods in the classification of non-Kählerian surfaces

@article{AndreiTeleman2009,
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 [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.},
author = {Andrei Teleman},
journal = {Banach Center Publications},
keywords = {complex surface; non-Kähler; instanton; stable bundle; class VII},
language = {eng},
number = {1},
pages = {109-120},
title = {Gauge theoretical methods in the classification of non-Kählerian surfaces},
url = {http://eudml.org/doc/281618},
volume = {85},
year = {2009},
}

TY - JOUR
AU - Andrei Teleman
TI - Gauge theoretical methods in the classification of non-Kählerian surfaces
JO - Banach Center Publications
PY - 2009
VL - 85
IS - 1
SP - 109
EP - 120
AB - 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.
LA - eng
KW - complex surface; non-Kähler; instanton; stable bundle; class VII
UR - http://eudml.org/doc/281618
ER -