Mathematics – Algebraic Geometry
Scientific paper
1999-10-22
Mathematics
Algebraic Geometry
36 pages, Plain-TeX (reason for resubmission: correction of one of the final numerical examples of K\"ahler-Einstein Del Pezzo
Scientific paper
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 K\"ahler-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 K\"ahler-Einstein Del Pezzo surfaces with quotient singularities are obtained.
Demailly Jean-Pierre
Kollár János
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