On the Milnor fibres of initial forms of topologically equivalent holomorphic functions
Abstract
Abstract Budur, Fernández de Bobadilla, Le, and Nguyen in 2022 conjectured that if two germs of holomorphic functions are topologically equivalent, then the Milnor fibres of their initial forms are homotopy equivalent. In this paper, we give an affirmative answer to this conjecture in the case of plane curves. We also show that a positive answer to this conjecture implies a positive answer to the famous Zariski multiplicity conjecture, both in the case of right equivalence and in the case of hypersurfaces with isolated singularities. Several other partial answers to these conjectures are also presented here.
Fields of Study & Subjects
Geometry and complex manifolds
Algebraic Geometry and Number Theory
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 6
- Publication date
- 1 June 2026
- Language
- EN