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Singular Gauduchon metrics

Part of: Analytic spaces Global differential geometry Families, fibrations

Published online by Cambridge University Press:  17 August 2022

Chung-Ming Pan
Chung-Ming Pan*
Affiliation:
Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, UPS, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France Chung_Ming.Pan@math.univ-toulouse.fr
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Abstract

In 1977, Gauduchon proved that on every compact hermitian manifold $(X, \omega )$ there exists a conformally equivalent hermitian metric $\omega _\mathrm {G}$ which satisfies $\mathrm {dd}^{\mathrm {c}} \omega _\mathrm {G}^{n-1} = 0$. In this note, we extend this result to irreducible compact singular hermitian varieties which admit a smoothing.

Keywords

Gauduchon metricscomplex spacessmoothable singularities

MSC classification

Primary: 53C55: Hermitian and Kählerian manifolds
Secondary: 14D06: Fibrations, degenerations 32C15: Complex spaces 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
Type
Research Article
Information
Compositio Mathematica , Volume 158 , Issue 6 , June 2022 , pp. 1314 - 1328
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Copyright
© 2022 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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