Singular

D.15.6 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.15.6.1 Vfiltration

compute

-generators for the 

-filtration on 

 truncated up to degree 

 in 

.

D.15.6.2 hodgeIdeals

compute the Hodge ideals of

 up to level 

, for a reduced hypersurface 

.

D.15.6.3 multIdeals

compute the multiplier ideals of a hypersurface

.

D.15.6.4 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 

.