## An algorithm for Hodge ideals

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Guillem Blanco
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## Abstract:

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.## References

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## Additional Information

**Guillem Blanco**- Affiliation: Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
- MR Author ID: 1308706
- Email: guillem.blanco@kuleuven.be
- 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: https://doi.org/10.1090/mcom/3764
- MathSciNet review: 4473109