Proves topological right-triviality for every holomorphic one-parameter family of isolated hypersurface singularities in ℂ3 with constant Milnor number, resolving the surface case of the μ-constant problem. After shrinking the parameter disk and representatives, ambient homeomorphisms vary jointly continuously, fix the origin section and preserve the defining functions.
Manuscript
Topological triviality of mu-constant families of surface singularities
September 24, 2026 · source · cite as \cite{OAI:Topological-triviality-of-mu-constant-families-of-surface-singularities-September-24-2026}
We prove that every holomorphic one-parameter family of isolated hypersurface singularities in ℂ3 with constant Milnor number is topologically right-trivial. This gives a positive answer to the surface case of the μ-constant problem. The trivialization fixes the parameter and the origin section, and preserves the defining functions.
Result 064 · Algebraic and complex geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md