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arXiv · 2103.07219

Families of ICIS with constant total Milnor number

Rafaela Soares de Carvalho·Juan José Nuño-Ballesteros·Bruna Oréfice-Okamoto·João Nivaldo Tomazella
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Abstract

We show that a family of isolated complete intersection singularities (ICIS) with constant total Milnor number has no coalescence of singularities. This extends a well known result of Gabrielov, Lazzeri and L\^e for hypersurfaces. We use A'Campo's theorem to see that the Lefschetz number of the generic monodromy of the ICIS is zero when the ICIS is singular. We give a pair applications for families of functions on ICIS which extend also some known results for functions on a smooth variety.

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Rafaela Soares de Carvalho, Juan José Nuño-Ballesteros, Bruna Oréfice-Okamoto, João Nivaldo Tomazella. 2021-03-12. Families of ICIS with constant total Milnor number. https://arxiv.org/abs/2103.07219

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