Non-minimal scalar-flat Kähler surfaces and parabolic stability
Non-minimal scalar-flat Kähler surfaces and parabolic stability
复制标题
非最小标量平坦凯勒曲面和抛物线稳定性
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
M. Singer
中科院分区：
文献类型：
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作者：
Yann Rollin;M. Singer
给出了非极小直纹曲面上标量平坦Kähler度量的一种新构造。该方法是基于orbifold直纹曲面的奇异性的解决方案，这是密切相关的秩-2抛物稳定的全纯丛。这个相当一般的构造也给出了低亏格的新例子：特别地，它证明了在10个适当选择的点上爆破的$mathbb{CP}^2 $允许标量平坦的凯勒度量;这回答了克劳德·勒布朗在1986年提出的一个与紧致自对偶4-流形的分类有关的问题。
A new construction is presented of scalar-flat Kähler metrics on non-minimal ruled surfaces. The method is based on the resolution of singularities of orbifold ruled surfaces which are closely related to rank-2 parabolically stable holomorphic bundles. This rather general construction is shown also to give new examples of low genus: in particular, it is shown that $mathbb{CP}^2$ blown up at 10 suitably chosen points, admits a scalar-flat Kähler metric; this answers a question raised by Claude LeBrun in 1986 in connection with the classification of compact self-dual 4-manifolds.