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Variation of numerical dimension of singular hermitian line bundles

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arxiv 1811.04385 v1 pith:3NDTRJX6 submitted 2018-11-11 math.AG math.CV

Shin-ichi Matsumura This is my paper · ORCID
classification math.AGmath.CV
keywords bundlesdimensionhermitianlinenumericalsingulartheoremvanishing
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The purpose of this paper is to give two supplements for vanishing theorems: One is a relative version of the Kawamata-Viehweg-Nadel type vanishing theorem, which is obtained from an observation for the variation of the numerical dimension of singular hermitian line bundles. The other is an analytic injectivity theorem for log canonical pairs on surfaces, which can be seen as a partial answer for Fujino's conjecture.

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  1. Analytic Bertini theorem II --- The local case

    math.AG 2026-07 accept novelty 8.0 of 10

    The local analytic Bertini theorem holds: multiplier ideal sheaves of psh functions on polydisc products restrict to fibers outside a pluripolar set.

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