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arXiv · 2405.12974

On the analytic structure of double and triple points in the target of finite holomorphic multi-germs

Juan J. Nuño-Ballesteros·Guillermo Peñafort Sanchis·Cinzia Villa
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Abstract

We study the analytic structure of the double and triple point spaces $M_2(f)$ and $M_3(f)$ of finite multi-germs $f\colon (X,S)\to(\mathbb{C}^{n+1},0)$, based on results of Mond and Pellikaan for the mono-germ case. We show that these spaces are Cohen-Macaulay, provided that certain dimensional conditions are satisfied, and give explicit expressions for their defining ideals in terms of those of their mono-germ branches.

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Juan J. Nuño-Ballesteros, Guillermo Peñafort Sanchis, Cinzia Villa. 2024-05-21. On the analytic structure of double and triple points in the target of finite holomorphic multi-germs. https://arxiv.org/abs/2405.12974

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