naa a22 4500 510810845 CHVBK 20180411083441.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s12220-012-9314-4 doi (NATIONALLICENCE)springer-10.1007/s12220-012-9314-4 Rashkovskii Alexander Tek/Nat, University of Stavanger, 4036, Stavanger, Norway aut Multi-circled Singularities, Lelong Numbers, and Integrability Index [Elektronische Daten] [Alexander Rashkovskii] By comparing Green functions of multi-circled plurisubharmonic singularities u in ℂ n to their indicators, we prove formulas for higher Lelong numbers L k (u) and integrability index λ u (the latter one being due to Kiselman) and extend Howald's result on multiplier ideals for monomial ideals to multi-circled singularities. This also leads to an elementary proof of the relations λ u ≤k -1 L k (u)1/k , 1≤k≤l, for the multi-circled singularities, where l is the codimension of the set u -1(-∞). For k=1 and arbitrary plurisubharmonic function u the inequality is due to Skoda, and for k=n and any plurisubharmonic u with isolated singularity the relation is due to Demailly. We also describe all multi-circled functions for which the inequalities are equalities. We also prove these inequalities, by a reduction to Demailly's result, in the general case of (not necessarily multi-circled) plurisubharmonic functions. In addition, we get a description of all plurisubharmonic singularities u whose integrability index is given by the lower bound in Skoda's inequality, i.e., λ u =n -1 L 1(u). Mathematica Josephina, Inc., 2012 Plurisubharmonic singularity nationallicence Lelong number nationallicence Monge-Ampère operator nationallicence Integrability index nationallicence Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/4(2013-10-01), 1976-1992 1050-6926 23:4<1976 2013 23 12220 https://doi.org/10.1007/s12220-012-9314-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-012-9314-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rashkovskii Alexander Tek/Nat, University of Stavanger, 4036, Stavanger, Norway aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/4(2013-10-01), 1976-1992 1050-6926 23:4<1976 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer