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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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An algorithm for Hodge ideals
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by Guillem Blanco HTML | PDF
Math. Comp. 91 (2022), 2955-2967 Request permission


We present an algorithm to compute the Hodge ideals (see M. Mustaţă and M. Popa [Mem. Amer. Math. Soc. 262 (2019), pp. v + 80; J. Éc. polytech. Math. 6 (2019), pp. 283–328]) of $\mathbb {Q}$-divisors associated to any reduced effective divisor $D$. The computation of the Hodge ideals is based on an algorithm to compute parts of the $V$-filtration of Kashiwara and Malgrange on $\iota _{+}\mathscr {O}_X(*D)$ and the characterization (see M. Mustaţă and M. Popa [Forum Math. Sigma 8 (2020), p. 41]) of the Hodge ideals in terms of this $V$-filtration. In particular, this gives a new algorithm to compute the multiplier ideals and the jumping numbers of any effective divisor.
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Additional Information
  • Guillem Blanco
  • Affiliation: Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
  • MR Author ID: 1308706
  • Email:
  • Received by editor(s): November 16, 2021
  • Received by editor(s) in revised form: May 24, 2022
  • Published electronically: July 27, 2022
  • Additional Notes: The author was supported by a Postdoctoral Fellowship of the Research Foundation – Flanders
  • © Copyright 2022 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 2955-2967
  • MSC (2020): Primary 14F10, 32C38, 14Q20, 32S40
  • DOI:
  • MathSciNet review: 4473109