421 research outputs found
estimates and vanishing theorems for holomorphic vector bundles equipped with singular Hermitian metrics
We investigate singular Hermitian metrics on vector bundles, especially
strictly Griffiths positive ones. esitimates and vanishing theorems
usually require an assumption that vector bundles are Nakano positive. However
there is no general definition of the Nakano positivity in singular settings.
In this paper, we show various estimates and vanishing theromes by
assuming that the vector bundle is strictly Griffiths positive and the base
manifold is projective.Comment: 19 page
Pseudonorms on direct images of pluricanonical bundles
We study pseudonorms on pluricanonical bundles over Stein manifolds. We prove
that the pseudonorms determine holomorphic structures of Stein manifolds under
certain assumptions. This theorem is a generalization of the result obtained by
Deng, Wang, Zhang, and Zhou for bounded domains in . We also
investigate Stein morphisms and the pseudonorms on direct images of
pluricanonical bundles. Our main goal in this paper is to show that the
pseudonorms also determine holomorphic structures of Stein morphisms. One
important technique is an -variant of the Ohsawa-Takegoshi extension
theorem.Comment: 18 page
Nakano positivity of singular Hermitian metrics and vanishing theorems of Demailly-Nadel-Nakano type
In this article, we propose a definition of Nakano semi-positivity of
singular Hermitian metrics on holomorphic vector bundles. By using this
positivity notion, we establish -estimates for holomorphic vector bundles
with Nakano positive singular Hermitian metrics. We also show vanishing
theorems, which generalize both Nakano type and Demailly-Nadel type vanishing
theorems. As applications, we specifically construct globally Nakano
semi-positive singular Hermitian metrics for several bundles, and prove
vanishing theorems associated with them.Comment: 28pages, v3: major revision. Theorem 1.7, 1.8, Subsection 2.3 and
Section 6 were adde
From Hörmander’s -estimates to partial positivity
In this article, using a twisted version of Hörmander’s -estimate, we give new characterizations of notions of partial positivity, which are uniform -positivity and RC-positivity. We also discuss the definition of uniform -positivity for singular Hermitian metrics
From Hörmander’s -estimates to partial positivity
In this article, using a twisted version of Hörmander’s -estimate, we give new characterizations of notions of partial positivity, which are uniform -positivity and RC-positivity. We also discuss the definition of uniform -positivity for singular Hermitian metrics
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