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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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