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D.15.7 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 $f \in R$.
The implemented algorithm [Bla21] is based on the characterization of the Hodge ideals in terms of the $V$-filtration of Malgrange and Kashiwara on $R_f f^s$, 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.15.7.1 Vfiltration  compute

-generators for the 

-filtration on 

 truncated up to degree 

 in 

.
D.15.7.2 hodgeIdeals  compute the Hodge ideals of

 up to level 

, for a reduced hypersurface 

.
D.15.7.3 multIdeals  compute the multiplier ideals of a hypersurface

.
D.15.7.4 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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