Upper Bounds for Roots of -Functions, following Kashiwara and Lichtin

  • Bradley Dirks

    University of Michigan, Ann Arbor, USA
  • Mircea Mustaţă

    University of Michigan, Ann Arbor, USA
Upper Bounds for Roots of $b$-Functions, following Kashiwara and Lichtin cover

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Abstract

By building on a method introduced by Kashiwara (Invent. Math. 38 (1976/77), 33–53) and refined by Lichtin (Ark. Mat. 27 (1989), 283–304), we give upper bounds for the roots of certain -functions associated to a regular function in terms of a log resolution of singularities. As applications, we recover with more elementary methods a result of Budur and Saito (J. Algebraic Geom. 14 (2005), 269–282) describing the multiplier ideals of in terms of the -filtration of and a result of the second-named author with Popa (Forum Math. Sigma 8 (2020), Paper No. e19, 41) giving a lower bound for the minimal exponent of in terms of a log resolution.

Cite this article

Bradley Dirks, Mircea Mustaţă, Upper Bounds for Roots of -Functions, following Kashiwara and Lichtin. Publ. Res. Inst. Math. Sci. 58 (2022), no. 4, pp. 693–712

DOI 10.4171/PRIMS/58-4-2