MultiplierIdealsDim2 -- A package for Multiplier Ideals

Description

MultiplierIdealsDim2 is a package that contains several tools related with the computations of multiplier ideals. Given the self intersection matrix and the divisor associated to this ideal, using the function MultiplierIdeals, one can compute the jumping numbers and their associated multiplier ideals in the interval (SmallestJN,BiggestJN] using either the algorithms presented on [Tuc10], [AAD14] or [AADG14]. However, if we want to know the multiplicity of a given number as a jumping number for a given ideal, one can use MultiplicityJN. Another option that this package offers is to compute the Multiplier Ideal associated to a given number, thanks to the function MultIdeal. The package also contains two extra functions: to compute the relative Canonical divisor of a resolution (RelativeCanonicalDivisor). And to compute the antinef closure of a given divisor (Unloading).

Literature

[AAD14] Multiplier ideals in two-dimensional local rings with rational singularities (M. Alberich-Carramiñana, J. Àlvarez Montaner, F. Dachs-Cadefau, 2014).
[AADG14] Poincaré series of multiplier ideals in two-dimensional local rings with rational singularities (M. Alberich-Carramiñana, J. Àlvarez Montaner, F. Dachs-Cadefau, V. González-Alonso, 2014)
[Tuc10] Jumping numbers on algebraic surfaces with rational singularities (K. Tucker, 2010)

Author

Ferran Dachs-Cadefau <[email protected]>

Version

This documentation describes version 1.0 of MultiplierIdealsDim2.

Source code

The source code from which this documentation is derived is in the file MultiplierIdealsDim2.m2.

Exports

Functions and commands
- MultIdeal -- Computes the multiplier ideal of a given number.
- MultiplicityJN -- Computes the multiplicity as a jumping number.
- MultiplierIdeals -- Computes the jumping numbers and their ideals
- RelativeCanonicalDivisor -- computes the relative canonical divisor
- Unloading -- Computes the antinef closure of a divisor.
Symbols
- algorithm -- Method used to compute the jumping numbers and multiplier ideals
- BiggestJN -- Upper bound of the interval where we want to compute the JN.
- JNandMI -- HashTable containing all the information about the Jumping Numbers
- JumpingDivisor -- Show or not the jumping divisors.
- MaxIterations -- Limits the number of iterations of the Unloading algorithm.
- SmallestJN -- Lower bound of the interval where we want to compute the JN.
- UnloadingValue -- Show the maximum of the unloaded values

For the programmer

The object MultiplierIdealsDim2 is a package.