### D.15.9 hodge_lib

Library:
  hodge.lib
Purpose:
  Algorithms for Hodge ideals

Authors:
  Guillem Blanco, email: guillem.blanco@kuleuven.be

Overview:
  A library for computing the Hodge ideals [MP19] of Q-divisors associated to any reduced hypersurface .
  The implemented algorithm [Bla21] is based on the characterization of the Hodge ideals in terms of the -filtration of Malgrange and Kashiwara on , see [MP20].
  As a consequence, this library provides also an algorithm to compute the multiplier ideals and the jumping numbers of any hypersurface, see [BS05].

References:
  [Bla21] G. Blanco, An algorithm for Hodge ideals, to appear.
  [BS05] N. Budur, M. Saito, Multiplier ideals, V-filtration, and spectrum, J. Algebraic Geom. 14 (2005), no. 2, 269-282. 2, 4
  [MP19] M. Mustata, M. Popa: Hodge ideals, Mem. Amer. Math. Soc. 262 (2019), no. 1268
  [MP20] M. Mustata, M. Popa: Hodge ideals for Q-divisors, V-filtration, and minimal exponent, Forum Math. Sigma 8 (2020), no. e19, 41 pp.

Procedures:

> D.15.9.1 Vfiltration |  | compute

> -generators for the
> -filtration on
> truncated up to degree
> in
> .

> D.15.9.2 hodgeIdeals |  | compute the Hodge ideals of

> up to level
> , for a reduced hypersurface
> .

> D.15.9.3 multIdeals |  | compute the multiplier ideals of a hypersurface

> .

> D.15.9.4 nextHodgeIdeal |  | given the

> -th Hodge ideal
> of
> compute the
> -th Hodge ideal assuming that the Hodge filtration of the underlying mixed Hodge module is generated at level less than or equal to
> .

See also: dmodapp_lib.

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