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Spectrum and multiplier ideals of arbitrary subvarieties. (English. French summary) Zbl 1241.32025
The relation between the spectrum of hypersurface singularities and the \(b\)-function and multiplier ideals has been studied by N. Budur [Math. Ann. 327, No. 2, 257–270 (2003; Zbl 1035.14010)] and M. Saito [Adv. Stud. Pure Math. 54, 355–379 (2009; Zbl 1171.14002)]. Multiplier ideals were originally defined for subvarieties of smooth varieties. This paper defines a spectrum for arbitrary subvarieties, generalising the definition of Steenbrink for hypersurfaces. The spectrum is shown to be essentially independent of the embedding. For an isolated complete intersection it coincides with the one given by W. Ebeling and J. H. M. Steenbrink [J. Algebr. Geom. 7, No. 1, 55–76 (1998; Zbl 0945.14003)], except for the coefficients of integral exponents. The relation to the graded pieces of the multiplier ideals is studied using the \(V\)-filtration of Kashiwara and Malgrange.
For monomial ideals a combinatorial description of the spectrum is given.

MSC:
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
32S35 Mixed Hodge theory of singular varieties (complex-analytic aspects)
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