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].
Arezzo, C., Della Vedova, A., Shi, Y. (2023). Constant scalar curvature Kähler metrics on ramified Galois coverings. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 2023(799), 229-247 [10.1515/crelle-2023-0026].
Constant scalar curvature Kähler metrics on ramified Galois coverings
Della Vedova A.
;
2023
Abstract
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].
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
