Abstract
We prove a regularity result for Monge–Ampère equations degenerate along smooth divisor on Kähler manifolds in Donaldson’s spaces of \(\beta \)-weighted functions. We apply this result to study the curvature of Kähler metrics with conical singularities and give a geometric sufficient condition on the divisor for its boundedness.
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Acknowledgements
We wish to thank S. Donaldson for having shared some of his ideas on this problem with the first author. The first author was partially supported by the FIRB Project “Geometria Differenziale Complessa e Dinamica Olomorfa”, while the second author was supported by the Marie Curie IOF Grant 255579 (CAMEGEST).
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Arezzo, C., Della Vedova, A. & La Nave, G. On the Curvature of Conic Kähler–Einstein Metrics. J Geom Anal 28, 265–283 (2018). https://doi.org/10.1007/s12220-017-9819-y
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DOI: https://doi.org/10.1007/s12220-017-9819-y