An algorithm for Hodge ideals

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 Q \mathbb {Q} -divisors associated to any reduced effective divisor D D . The computation of the Hodge ideals is based on an algorithm to compute parts of the V V -filtration of Kashiwara and Malgrange on ι + O X ( ∗ D ) \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 V -filtration. In particular, this gives a new algorithm to compute the multiplier ideals and the jumping numbers of any effective divisor.