Open Access
February 2018 Resolution of the canonical fiber metrics for a Lefschetz fibration
Richard Melrose, Xuwen Zhu
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J. Differential Geom. 108(2): 295-317 (February 2018). DOI: 10.4310/jdg/1518490819


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.


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Richard Melrose. Xuwen Zhu. "Resolution of the canonical fiber metrics for a Lefschetz fibration." J. Differential Geom. 108 (2) 295 - 317, February 2018.


Received: 7 July 2015; Published: February 2018
First available in Project Euclid: 13 February 2018

zbMATH: 06846979
MathSciNet: MR3763069
Digital Object Identifier: 10.4310/jdg/1518490819

Rights: Copyright © 2018 Lehigh University

Vol.108 • No. 2 • February 2018
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