{"id":"openai-math/Ambiently-homeomorphic-isolated-hypersurface-germs-in-C4-with-multiplicities-four-and-five","pdf":"https://github.com/openai/math/blob/main/preprints/Ambiently-homeomorphic-isolated-hypersurface-germs-in-C4-with-multiplicities-four-and-five-September-27-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Ambiently-homeomorphic-isolated-hypersurface-germs-in-C4-with-multiplicities-four-and-five-September-27-2026","tags":["singularity-theory","algebraic-geometry"],"score":0,"title":"Ambiently homeomorphic isolated hypersurface germs in ℂ⁴ with multiplicities four and five","domain":"Algebraic and complex geometry","family":"059","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We give a negative answer to Zariski's multiplicity question in four complex variables. We construct two reduced convergent holomorphic function germs with isolated critical points and multiplicities four and five whose zero-set germs are ambiently homeomorphic.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":false,"family_title":"Counterexamples to Zariski’s multiplicity conjecture"}