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

Tadeusz Krasiński; Justyna Walewska

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arXiv · 1803.05324

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

Tadeusz Krasiński·Justyna Walewska

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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.

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BibTeX RIS

Tadeusz Krasiński, Justyna Walewska. 2018-03-13. Jumps of Milnor numbers of Brieskorn-Pham singularities in non-degenerate families. https://arxiv.org/abs/1803.05324

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