Resolution of the canonical fiber metrics for a lefschetz fibration
Name
1501.04124.pdf
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243.83 KB
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Author(s)
Melrose, Richard B
Zhu, Xuwen
Date Issued
June 2016
Journal
Journal of differential geometry
Publisher
International Press of Boston, Inc.
Citation
Melrose, Richard and Xuwen Zhu. "Resolution of the canonical fiber metrics for a Lefschetz fibration." Journal of Differential Geometry, 108 (2018), pp. 295--317.
Version
Original manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://projecteuclid.org/euclid.jdg/1518490819
