Equivalence of plurisubharmonic singularities and Siu-type metrics
arXiv:1407.6474
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.
The statement of Corollary 4.4 corrected to include bigness which was missing