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

2024/05/21 by J. J. Nuño‐Ballesteros, Nuño-Ballesteros, Juan J., Guillermo Peñafort Sanchis +3
Mathematics · #13C14 #14B05 #14J17 #32S25 #58K20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Approximation and Integration #Meromorphic and Entire Functions #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2405.12974

openalex publication_date 2024/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the analytic structure of the double and triple point spaces M₂(f) and M₃(f) of finite multi-germs f\colon (X,S)→(ℂⁿ⁺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.

Related

• Multiple point spaces of finite holomorphic maps
• Vanishing Topology of Codimension 1 Multi-germs over \Bbb R and \Bbb C
• Vanishing topology of codimension 1 multi-germs over R and C
• Monomial Multiple Structures
• Examples of finitely determined map-germs of corank 3 supporting Mond's μ≥ τ-type conjecture