Good real pictures of corank one map germs from the n-space to the (n+1)-space

2025/07/17 by R. Giménez Conejero, Conejero, R. Giménez, Ignacio Breva Ribes +1
Computer Science · Mathematics · #32S30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Primary 58K60 #Secondary 14P25 #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2507.13467

openalex publication_date 2025/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study corank one A-finite germs f:(ℝⁿ,0)→ (ℝⁿ⁺¹,0) and their complexifications. More precisely, we study when these germs provide good real pictures of the complex germs, i.e., when there is a real deformation that has the same homology in the image (hence, homotopy) than the generic complex deformation. We give a new sufficient condition that can be computed in practice, as well as examples.

Citations

• Good real images of complex maps
• The image Milnor number and excellent unfoldings
• Multiple points of a simplicial map and image-computing spectral sequences
• Stratification of Unfoldings of Corank 1 Singularities
• Vanishing topology of codimension 1 multi-germs over R and C
• Le groupe de monodromie du déploiement des singularités isolées de courbes planes I

Related

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• Vanishing topology of codimension 1 multi-germs over R and C
• Examples of finitely determined map-germs of corank 3 supporting Mond's μ≥ τ-type conjecture
• Disentanglements of corank 2 map-germs: two examples