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On \(b\)-function, spectrum and multiplier ideals. (English) Zbl 1171.14002

Miwa, Tetsuji (ed.) et al., Algebraic analysis and around in honor of Professor Masaki Kashiwara’s 60th birthday. Tokyo: Mathematical Society of Japan (ISBN 978-4-931469-51-8/hbk). Advanced Studies in Pure Mathematics 54, 355-379 (2009).
Singularity theory has many different aspects and connections with various fields in mathematics. It has been observed that many different point of views on singularities are in fact related. In this expository article, the author gives a concise survey of three different singularity invariants: \(b\)-functions, or Bernstein-Sato polynomials, coming from differential equations; Hodge spectrum, dealing with classical invariants such as the Milnor fiber and monodromy; and multiplier ideals, coming from higher-dimensional algebraic geometry and differential geometry. An important part of the survey consists of the various relations among these invariants, and how to compute them in some specific cases.
For the entire collection see [Zbl 1160.32002].

MSC:

14B05 Singularities in algebraic geometry
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
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