Resolution of the canonical fiber metrics for a Lefschetz fibration
Resolution of the canonical fiber metrics for a Lefschetz fibration
复制标题
Lefschetz 纤维规范纤维度量的分辨率
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Xuwen Zhu
中科院分区：
文献类型：
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作者：
R. Melrose;Xuwen Zhu
我们考虑 Lefschetz 纤维的常曲率纤维度量族，其属规则纤维大于 1。 Obitsu 和 Wolpert 的结果经过精炼，表明在通过迭代爆炸构建的总空间的适当分辨率上，该族是对数平滑的，即具有积分幂但可能具有多重性的多齐性，在尺寸参数方面与收缩测地线长度的对数相当。
We consider the family of constant curvature fiber metrics for a Lefschetz fibration with regular fibers of genus greater than one. A result of Obitsu and Wolpert is refined by showing that on an appropriate resolution of the total space, constructed by iterated blow-up, this family is log-smooth, i.e. polyhomogeneous with integral powers but possible multiplicities, at the preimage of the singular fibers in terms of parameters of size comparable to the logarithm of the length of the shrinking geodesic.