Jumps of Milnor numbers of Brieskorn-Pham singularities in non-degenerate families

Abstract

The jump of the Milnor number of an isolated singularity $f_0$ is the minimal non-zero difference between the Milnor numbers of $f_0$ and one of its deformation $(f_s).$ In the case $f_s$ are non-degenerate singularities we call the jump non-degenerate. We give a formula (an inductive algorithm using diophantine equations) for the non-degenerate jump of $f_0$ in the case $f_0$ is a convenient singularity with only one $(n-1)$-dimensional face of its Newton diagram which equivalently (in our problem) can be replaced by the Brieskorn-Pham singularities.

10 pages, 1 figure. arXiv admin note: text overlap with arXiv:1508.02704