Singular Manual: hodge_lib

> | ### 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 674#674. The implemented algorithm [Bla21] is based on the characterization of the Hodge ideals in terms of the 322#322-filtration of Malgrange and Kashiwara on 1065#1065, 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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