An algorithm for Hodge ideals

Blanco, Guillem

doi:10.1090/mcom/3764

An algorithm for Hodge ideals
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by Guillem Blanco;

Math. Comp. 91 (2022), 2955-2967

DOI: https://doi.org/10.1090/mcom/3764

Published electronically: July 27, 2022

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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.

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