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arXiv · 1407.6474

Equivalence of plurisubharmonic singularities and Siu-type metrics

Dano Kim
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Abstract

We show by an example that the (equivalence class of) singularity of a plurisubharmonic function cannot be determined by the data of its Lelong numbers, in a nontrivial sense. Such an example is provided by Siu-type singular hermitian metrics associated to an effective line bundle. We also show that a Siu-type metric has analytic singularities if and only if the section ring of the line bundle is finitely generated.

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Dano Kim. 2014-10-19. Equivalence of plurisubharmonic singularities and Siu-type metrics. https://arxiv.org/abs/1407.6474

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