Families of ICIS with constant total Milnor number

2021/03/12 by R. S. Carvalho, de Carvalho, Rafaela Soares, J. J. Nuño‐Ballesteros +5
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2103.07219

openalex publication_date 2021/03/12 · openalex created_date 2021/03/29 · openalex updated_date 2026/07/28

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 Lê 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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