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Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds | | Jean-Pierre Demailly
; János Kollár
; | | Date: |
22 Oct 1999 | | Subject: | Algebraic Geometry MSC-class: 14B05, 14J45, 32C17, 32J25, 32S05 | math.AG | | Abstract: | We introduce complex singularity exponents of plurisubharmonic functions and prove a general semi-continuity result for them. This concept contains as a special case several similar concepts which have been considered e.g. by Arnold and Varchenko, mostly for the study of hypersurface singularities. The plurisubharmonic version is somehow based on a reduction to the algebraic case, but it also takes into account more quantitative informations of great interest for complex analysis and complex differential geometry. We give as an application a new derivation of criteria for the existence of Kähler-Einstein metrics on certain Fano orbifolds, following Nadel’s original ideas (but with a drastic simplication in the technique, once the semi-continuity result is taken for granted). In this way, 3 new examples of rigid Kähler-Einstein Del Pezzo surfaces with quotient singularities are obtained. | | Source: | arXiv, math.AG/9910118 | | Services: | Forum | Review | PDF | Favorites | |
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