English

Equivalence of plurisubharmonic singularities and Siu-type metrics

Complex Variables 2014-10-21 v2 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.1407.6474,
  title  = {Equivalence of plurisubharmonic singularities and Siu-type metrics},
  author = {Dano Kim},
  journal= {arXiv preprint arXiv:1407.6474},
  year   = {2014}
}

Comments

The statement of Corollary 4.4 corrected to include bigness which was missing