2023/07/10 by Krzysztof Jan Nowak, Nowak, Krzysztof Jan
Mathematics · #32S05 #32S65 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2307.05226
openalex publication_date 2023/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The following pullback problem will be considered. Given a finite holomorphic map germ ϕ: (ℂn, 0) → (ℂn, 0) and an analytic germ X in the target, if the preimage Y = ϕ-1(X), taken with the reduced structure, is smooth, so is X. The main aim of this paper is to give an affirmative solution for X being a geometric complete intersection. The case, where Y is not contained in the ramification divisor Z of ϕ, was established by Ebenfelt-Rothschild (2007) and afterwards by Lebl (2008) and Denkowski (2016). The hypersurface case was achieved by Giraldo-Roeder (2020) and recently by Jelonek (2023).