Family 064Algebraic and complex geometryNo LeanNot yet digested
Topological triviality of μ-constant surface singularities
Proves topological right-triviality for every holomorphic one-parameter family of isolated hypersurface singularities in ℂ 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.
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Topological triviality of mu-constant families of surface singularities
Sep 24, 2026·main.pdf
We prove that every holomorphic one-parameter family of isolated hypersurface singularities in ℂ 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.