zetaFunctionPoles

Implementation in Magma of an algorithm to calculate the stratification of $\mu$-constant plane branch deformations by the poles of the complex zeta function.

This is equivalent to the stratification by the roots of the Bernstein-Sato polynomial in the following cases:

• A plane branch deformation with pairwise different monodromy eigenvalues (this includes in particular the case of one characteristic exponent).
• A plane branch deformation for which the only coinciding candidates are of geometric origin (e.g. semigroup $\langle 10,15,36 \rangle$).

Plane branches can be considered as deformations with zero parameters, so this code can be used to calculate the set of poles (or the Bernstein-Sato polynomial in the previous cases) for a particular curve.

An article explaining the mathematical results in which the code is based will be published.

Requirements

• Install Magma (computer algebra system)
• Download SingularitiesDim2/ (library for plane curve singularities by Guillem Blanco)
• Download this repository

Files

• ZetaFunction/: library for computing the stratification by the poles by the poles of the complex zeta function
• usage/: my personal usage of the library; you may ignore its contents; the correctness of the computed examples is not guaranteed
• calculateExample.m: simple script to compute examples
• exampleOutput.txt: output of calculateExample.m

Usage example

See calculateExample.m.