Bekka's (c)-regularity condition and families of line singularities with constant Lê numbers

2025/08/20 by Eyral, Christophe, Turhan, Öznur
#14B05 #14B07 #32S05 #32S15 #32S25 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.14545

Abstract

We show that the natural stratifications arising from certain deformation families of line singularities with constant Lê numbers satisfy Bekka's (c)-regularity condition. As a corollary, we obtain that these families are topologically equisingular. Similar results for families of isolated singularities were established by Abderrahmane.

Citations

• Correction to : The Kuo condition, an inequality of Thom's type and (c)-regularity
• Lê numbers and Newton diagram
• Non-compact Newton boundary and Whitney equisingularity for non-isolated singularities
• On deformation with constant Milnor number and Newton polyhedron
• Topological Triviality of μ-constant Deformations of Type f(x) + tg(x)

Related

• Equisingularity of families of hypersurfaces and applications to mappings
• Topologically equisingular deformations of homogeneous hypersurfaces\n with line singularities are equimultiple
• Bounded deformations of (ε,δ)-log canonical singularities
• Topological equisingularity of function germs with 1-dimensional critical set
• Isolated singularities, smooth orders and Auslander regularity