Spectrum and multiplier ideals of arbitrary subvarieties (Q407803)

The relation between the spectrum of hypersurface singularities and the \(b\)-function and multiplier ideals has been studied by \textit{N. Budur} [Math. Ann. 327, No. 2, 257--270 (2003; Zbl 1035.14010)] and \textit{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 \textit{W. Ebeling} and \textit{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.NEWLINENEWLINEFor monomial ideals a combinatorial description of the spectrum is given.