On a generic symmetry defect hypersurface

2014/03/23 by S. Janeczko, Janeczko, S., Z. Jelonek +3
Mathematics · #Advanced Differential Equations and Dynamical Systems #Affine transformation #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic curve #Algebraic number #Combinatorics #Degree (music) #FOS: Mathematics #General position #Geometry #Hypersurface #Mathematical analysis #Mathematics #Meromorphic and Entire Functions #Physics #Polynomial #Pure mathematics #Symmetry (geometry) #math.AG

paper · pdf · doi:10.48550/arxiv.1403.5769

arxiv created 2014/03/23 · openalex publication_date 2014/03/23 · arxiv updated 2014/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f : X -> Y be a dominant polynomial mapping of affine varieties. For generic y in Y we have Sing(f^-1(y)) = f^-1(y) ∩ Sing(X): As an application we show that symmetry defect hypersurfaces for two generic members of the irreducible algebraic family of n-dimensional smooth irreducible subvarieties in general position in C²ⁿ are homeomorphic and they have homeomorphic sets of singular points. In particular symmetry defect curves for two generic curves in C² of the same degree have the same number of singular points.

Related

• Generic symmetry defect set of an algebraic curve
• Symmetry defect of n-dimensional complete intersections in ℂ^2n-1
• Defect of projective hypersurfaces with isolated singularities
• Isolated non-normal crossings
• Birational geometry of defective varieties, II