Asymptotically analytic and other plurisubharmonic singularities

Details Asymptotically analytic and other plurisubharmonic singularities Asymptotically analytic and other plurisubharmonic singularities

2009-10-12

arxiv.org/abs/0910.2137v1

Mathematics

Complex Variables

28 pages

Scientific paper

We study classes of singularities of plurisubharmonic functions that can be approximated by analytic singularities with control over the residual Monge-Ampere masses. They are characterized in terms of Demailly's approximations, graded families of ideals of analytic functions and their asymptotic multiplier ideals, as well as in terms of relative types. The types relative to such singularities are represented as lower envelopes of weighted divisorial valuations and of certain disk functionals. Finally, for functions with asymptotically analytic singularities we prove a Minkowski's type inequality for the residual Monge-Ampere masses and a plurisubharmonic variant of Mustata's summation formula for multiplier ideals.

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