MultiplierMeromorphic

Implementation in Magma of an algorithm to calculate multiplier ideals of meromorphic functions.

Requirements

• Install Magma
• Download this repository (the only necessary file is MultiplierMeromorphic.m)
• Download SingularitiesDim2/

Files

• MultiplierMeromorphic.m: functions to calculate log resolutions and multiplier ideals of meromorphic functions
• MultiplierMeromorphic.sig: file autogenerated by Magma
• calculateExamples.m: simple script to compute examples
• calculateExamplesFancy.m: complicated script to compute examples
• Examples/: computed examples

Usage example

Calculate the minimal log-resolution of $\frac{f}{g}$ and the multiplier ideals

$$\mathcal{J}\left(\left(\frac{f}{g}\right)^\lambda\right)$$

for

$$\begin{align*} &f = (y^2-x^3)^4 + x^8 y^5 , \\ &g = y^2-x^3 , \end{align*}$$

in the range $\lambda\in(0,2)$.

Magma

AttachSpec("./SingularitiesDim2/IntegralClosureDim2.spec");
Attach("./MultiplierMeromorphic.m");
P<x, y> := LocalPolynomialRing(RationalField(), 2, "lglex");
f := (y^2-x^3)^4 + x^8*y^5;
g := y^2-x^3;
Nf, Ng, N, Prox := LogResolutionMeromorphic(f, g);
S := MultiplierIdealsMeromorphic(f, g : MinJN:=0, MaxJN:=2, ComputeIdeals:=true);