Multiplier Submodule Sheaves and a problem of Lempert. arXiv:2111.13452
Preprint, arXiv:2111.13452 [math.CV] (2021).
Summary: In this article, we establish an \(L^2\) extension theorem for Nakano semi-positive singular Hermitian metrics on holomorphic vector bundles, and the strong openness and stability properties of the multiplier submodule sheaves associated to Nakano semi-positive singular Hermitian metrics on holomorphic vector bundles. We solve affirmatively a question of Lempert on the preservation of Nakano semi-positivity under limit of an increasing metrics based on Deng-Ning-Wang-Zhou’s characterization of Nakano positivity.
MSC:
| 32U05 | Plurisubharmonic functions and generalizations |
| 32E10 | Stein spaces |
| 32L10 | Sheaves and cohomology of sections of holomorphic vector bundles, general results |
| 32W05 | \(\overline\partial\) and \(\overline\partial\)-Neumann operators |
| 14F18 | Multiplier ideals |
| 14C30 | Transcendental methods, Hodge theory (algebro-geometric aspects) |
| 32L05 | Holomorphic bundles and generalizations |
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