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arXiv · 1810.09002

Image Milnor number formulas for weighted-homogeneous map-germs

Irma Pallarés Torres·Guillermo Peñafort Sanchis
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Abstract

We give formulas for the image Milnor number of a weighted-homogeneous map-germ $(\mathbb{C}^n,0)\to(\mathbb{C}^{n+1},0)$, for $n=4$ and $5$, in terms of weights and degrees. Our expressions are obtained by a purely interpolative method, applied to a result by Ohmoto. We use our approach to recover the formulas for $n=2$ and $3$ due to Mond and Ohmoto, respectively. For $n\geq 6$, the method is valid as long as certain multi-singularity conjecture holds.

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Irma Pallarés Torres, Guillermo Peñafort Sanchis. 2018-10-21. Image Milnor number formulas for weighted-homogeneous map-germs. https://arxiv.org/abs/1810.09002

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