A note on Bernstein–Sato ideals
DOI:
https://doi.org/10.33044/revuma.2795Abstract
We define the Bernstein-Sato ideal associated to a tuple of ideals and we relate it to the jumping points of the corresponding mixed multiplier ideals.
Downloads
References
J. Àlvarez Montaner, J. Jeffries and L. Núñez-Betancourt, Bernstein–Sato polynomials in commutative algebra, in Commutative Algebra, 1–76, Springer, Cham, 2021. MR 4394404.
J. Briançon and P. Maisonobe, Bernstein–Sato ideals associated to polynomials I, Unpublished notes, 2002.
J. Briançon and H. Maynadier, Équations fonctionnelles généralisées: transversalité et principalité de l'idéal de Bernstein–Sato, J. Math. Kyoto Univ. 39 (1999), no. 2, 215–232. MR 1709290.
N. Budur, Bernstein–Sato polynomials, Lecture notes for the summer school Multiplier Ideals, Test Ideals, and Bernstein–Sato Polynomials, at UPC Barcelona, 2015. Available at https://perswww.kuleuven.be/ u0089821/Barcelona/BarcelonaNotes.pdf.
N. Budur, M. Mustaţă and M. Saito, Bernstein–Sato polynomials of arbitrary varieties, Compos. Math. 142 (2006), no. 3, 779–797. MR 2231202.
N. Budur and M. Saito, Multiplier ideals, $V$-filtration, and spectrum, J. Algebraic Geom. 14 (2005), no. 2, 269–282. MR 2123230.
P. Cassou-Noguès and A. Libgober, Multivariable Hodge theoretical invariants of germs of plane curves, J. Knot Theory Ramifications 20 (2011), no. 6, 787–805. MR 2812263.
L. Ein, R. Lazarsfeld, K. E. Smith and D. Varolin, Jumping coefficients of multiplier ideals, Duke Math. J. 123 (2004), no. 3, 469–506. MR 2068967.
M. Granger, Bernstein–Sato polynomials and functional equations, in Algebraic Approach to Differential Equations, 225–291, World Sci. Publ., Hackensack, NJ, 2010. MR 2766095.
R. Lazarsfeld, Positivity in Algebraic Geometry. II, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, 49, Springer-Verlag, Berlin, 2004. MR 2095472.
H. Maynadier, Polynômes de Bernstein–Sato associés à une intersection complète quasi-homogène à singularité isolée, Bull. Soc. Math. France 125 (1997), no. 4, 547–571. MR 1630902.
M. Mustaţă, Bernstein–Sato polynomials for general ideals vs. principal ideals, Proc. Amer. Math. Soc. 150 (2022), no. 9, 3655–3662. MR 4446219.
M. Mustaţă and M. Popa, Hodge ideals and minimal exponents of ideals, Rev. Roumaine Math. Pures Appl. 65 (2020), no. 3, 327–354. MR 4216533.
C. Sabbah, Proximité évanescente. II. Équations fonctionnelles pour plusieurs fonctions analytiques, Compositio Math. 64 (1987), no. 2, 213–241. MR 0916482.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 Josep Àlvarez Montaner
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal. The Journal may retract the paper after publication if clear evidence is found that the findings are unreliable as a result of misconduct or honest error.
