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摘要翻译：
VII类曲面的分类是复杂几何中一个非常困难的经典问题。专家们认为它是Enriques-Kodaira复杂曲面分类表中最重要的一个缺口。关于这个问题的标准猜想指出，任何具有$B_2>0$的极小VII类曲面都有$B_2$曲线。根据Kato，Nakamura和Dloussky/Oeljeklaus/Toma的结果，该猜想（如果成立）将完全解决这个分类问题。基于Donaldson理论的技巧，我们解释了一种新的方法来证明VII类曲面上曲线的存在性，并给出了用这种方法得到的最新结果。
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英文标题：
《Gauge theoretical methods in the classification of non-Kaehlerian
surfaces》
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作者：
Andrei Teleman
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Complex Variables 复变数
分类描述：Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数，自守群作用与形式，伪凸性，复几何，解析空间，解析束
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Geometric Topology 几何拓扑
分类描述：Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures
流形，轨道，多面体，细胞复合体，叶状，几何结构
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英文摘要：
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 $b_2>0$ has $b_2$ 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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PDF链接：
https://arxiv.org/pdf/0804.0557
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