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On Hodge spectrum and multiplier ideals. (English) Zbl 1035.14010
The article relates the Hodge spectrum of a hypersurface singularity and the jumping number of the multiplier ideals of an effective divisor, computed at the singular point. The main result states that, under some mild restrictions, the multiplicities of the Hodge spectral numbers of a singular point and the respective inner jump multiplicities coincide. The proof relies on the motivic integration theory and the Denef-Loeser computation of the Hodge spectrum via the log resolution.

MSC:
14J17 Singularities of surfaces or higher-dimensional varieties
14B05 Singularities in algebraic geometry
32S35 Mixed Hodge theory of singular varieties (complex-analytic aspects)
14J70 Hypersurfaces and algebraic geometry
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
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