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Nov 2004 Constant scalar curvature Kähler metrics on fibred complex surfaces
Joel Fine
J. Differential Geom. 68(3): 397-432 (Nov 2004). DOI: 10.4310/jdg/1115669591


This article finds constant scalar curvature Kähler metrics on certain compact complex surfaces. The surfaces considered are those admitting a holomorphic submersion to curve, with fibres of genus at least 2. The proof is via an adiabatic limit. An approximate solution is constructed out of the hyperbolic metrics on the fibres and a large multiple of a certain metric on the base. A parameter dependent inverse function theorem is then used to perturb the approximate solution to a genuine solution in the same cohomology class. The arguments also apply to certain higher dimensional fibred Kähler manifolds.


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Joel Fine. "Constant scalar curvature Kähler metrics on fibred complex surfaces." J. Differential Geom. 68 (3) 397 - 432, Nov 2004.


Published: Nov 2004
First available in Project Euclid: 9 May 2005

zbMATH: 1085.53064
MathSciNet: MR2144537
Digital Object Identifier: 10.4310/jdg/1115669591

Rights: Copyright © 2004 Lehigh University


Vol.68 • No. 3 • Nov 2004
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