Constant scalar curvature Kähler metrics on ramified Galois coverings

We give sufficient conditions for the existence of Kahler-Einstein and constant scalar curvature Kahler (cscK) metrics on finite ramified Galois coverings of a cscK manifold in terms of cohomological conditions on the Kahler classes and the branching divisor. This result generalizes previous work on Kahler-Einstein metrics by Li and Sun [C. Li and S. Sun, Conical Kahler-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 Kahler metrics (II)-Existence results, J. Amer. Math. Soc. 34 2021, 4, 937-1009].