Griffiths and Nakano positivity and Nakano-Nadel vanishing theorems for singular Hermitian metrics on complex spaces

2026/06/15 by Yuta Watanabe
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 introduce appropriate notions of singular Griffiths/Nakano positivity on complex spaces and establish various properties of these notions. By applying these results, we provide L²-Dolbeault fine resolutions and cohomological isomorphisms, and L²-existence theorems. As an application, we obtain Nakano-Nadel vanishing theorems on weakly pseudoconvex complex spaces.

Citations

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

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