Constant scalar curvature Kähler metrics on ramified Galois coverings
-
Claudio Arezzo
and
Yalong Shi
Abstract
We give sufficient conditions for the existence of Kähler–Einstein and constant scalar curvature Kähler (cscK) metrics on finite ramified Galois coverings of a cscK manifold in terms of cohomological conditions on the Kähler classes and the branching divisor. This result generalizes previous work on Kähler–Einstein metrics by Li and Sun [C. Li and S. Sun, Conical Kähler–Einstein metrics revisited, Comm. Math. Phys. 331 2014, 3, 927–973], and extends Chen–Cheng’s existence results for cscK metrics in [X. Chen and J. Cheng, On the constant scalar curvature Kähler metrics (II)—Existence results, J. Amer. Math. Soc. 34 2021, 4, 937–1009].
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11871265
Funding statement: The third author is supported by NSFC No. 11871265.
Acknowledgements
The first author is very grateful to Fabio Perroni for his beautiful explanations of the Catanese–Perroni’s theory largely used in the last section to produce many interesting examples. The third author thanks K. Zheng for helpful discussions on conical metrics. This work began when the second and third authors were both visiting ICTP, they would like to thank ICTP for its hospitality.
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Articles in the same Issue
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- Geometric arcs and fundamental groups of rigid spaces
- Free boundary regularity in the multiple membrane problem in the plane
- 𝐾-invariant Hilbert modules and singular vector bundles on bounded symmetric domains
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- Constant scalar curvature Kähler metrics on ramified Galois coverings
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Articles in the same Issue
- Frontmatter
- Stable pair compactification of moduli of K3 surfaces of degree 2
- Geometric arcs and fundamental groups of rigid spaces
- Free boundary regularity in the multiple membrane problem in the plane
- 𝐾-invariant Hilbert modules and singular vector bundles on bounded symmetric domains
- Hodge theory on ALG∗ manifolds
- Constant scalar curvature Kähler metrics on ramified Galois coverings
- On fundamental groups of RCD spaces
- Geodesic nets on non-compact Riemannian manifolds
