Zero loci of Bernstein–Sato ideals

Zero loci of Bernstein–Sato ideals

We prove a conjecture of the first author relating the Bernstein–Sato ideal of a finite collection of multivariate polynomials with cohomology support loci of rank one complex local systems. This generalizes a classical theorem of Malgrange and Kashiwara relating the b -function of a multivariate po...

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Veröffentlicht in:Inventiones mathematicae 2021-07, Vol.225 (1), p.45-72
Hauptverfasser: Budur, Nero, van der Veer, Robin, Wu, Lei, Zhou, Peng
Format: Artikel
Sprache:eng
Schlagworte:
Eigenvalues
Homology
Loci
Mathematics
Mathematics and Statistics
Multivariate analysis
Polynomials
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Zusammenfassung:We prove a conjecture of the first author relating the Bernstein–Sato ideal of a finite collection of multivariate polynomials with cohomology support loci of rank one complex local systems. This generalizes a classical theorem of Malgrange and Kashiwara relating the b -function of a multivariate polynomial with the monodromy eigenvalues on the Milnor fibers cohomology.
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-020-01025-x