Some consequences of the μ-constant condition for families of surfaces

2023/12/01 by Marta Aldasoro Rosales, Rosales, Marta Aldasoro
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2312.00887

openalex publication_date 2023/12/01 · openalex created_date 2023/12/06 · openalex updated_date 2026/08/01

Abstract

Let f : X→ Δ be a 1-parameter family of 2-dimensional isolated hypersurface singularities. In this paper, we show that if the Milnor number is constant, then any semistable model, obtained from f after a sufficiently large base change must satisfy non trivial restrictions. Those restrictions are in terms of the dual complex, Hodge structure and numerical invariants of the central fibre.

Related

• On the topology of families of isolated singularities
• On deformation with constant Milnor number and Newton polyhedron
• The Milnor fibre signature is not semi-continuous
• Hypersurface Singularities and Milnor Equisingularity
• μ-constant monodromy groups and Torelli results for marked singularities, for the unimodal and some bimodal singularities