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arXiv · 2301.08989

Note on Milnor numbers of irreducible germs

Zbigniew Jelonek
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Abstract

Let $(\bf {V,0})\subset (\mathbb{C}^n,0)$ be a germ of a complex hypersurface and let $f: (\mathbb{C}^n,0)\to(\mathbb{C}^n,0)$ be a germ of a finite holomorphic mapping. If germs $(\bf {V,0})$ and ${\bf W}:=(F^{-1}(\bf{ V})),0)$ are irreducible and with isolated singularities, then $$\mu(F^{-1}(\bf{ V}))\ge \mu(\bf {V}),$$ where $\mu$ denotes the Milnor number.

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Zbigniew Jelonek. 2023-01-21. Note on Milnor numbers of irreducible germs. https://arxiv.org/abs/2301.08989

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