L²-Dolbeault resolutions and Nadel vanishing on weakly pseudoconvex complex spaces with singular Hermitian metrics

2026/02/03 by Yuta Watanabe · 2 citations
Mathematics · #math.CV

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Abstract

In this paper, in order to develop a more general L²-theory for the ∂-operator on complex spaces, we provide L²-Dolbeault fine resolutions and isomorphisms, and L²-estimates, for holomorphic line bundles on complex spaces equipped with singular Hermitian metrics. As applications, we obtain several generalizations of the Nadel vanishing theorem.

Cited by

• Griffiths and Nakano positivity and Nakano-Nadel vanishing theorems for singular Hermitian metrics on complex spaces
• Steenbrink vanishing theorem for big line bundles

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