Constant scalar curvature Kaehler metrics on ramified Galois coverings

Alberto Della Vedova; Claudio Arezzo; Yalong Shi

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Constant scalar curvature Kaehler metrics on ramified Galois coverings

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arxiv 2110.01222 v1 pith:RPC5MAWV submitted 2021-10-04 math.DG

Constant scalar curvature Kaehler metrics on ramified Galois coverings

Claudio Arezzo , Alberto Della Vedova , Yalong Shi This is my paper

classification math.DG

keywords metricscsckkaehlerconditionsconstantcoveringscurvatureexistence

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We give sufficient conditions for the existence of Kaehler-Einstein and constant scalar curvature Kaehler (cscK) metrics on finite ramified Galois coverings of a cscK manifold in terms of cohomological conditions on the Kaehler classes and the branching divisor. This result generalizes previous work on Kaehler-Einstein metrics by Li-Sun [Comm. Math. Phys. 2014], and extends Chen-Cheng's existence results for cscK metrics in [J. Amer. Math. Soc. 2021].

Constant scalar curvature Kaehler metrics on ramified Galois coverings

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