Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 059-01. Ambiently homeomorphic isolated hypersurfaces of multiplicities two and three
Manuscript map · lines 3695–3704
OpenAI@2026-10-07#rem:oai-p-059-01
Authors: OpenAI. Family 059.
Title: Ambiently homeomorphic isolated hypersurfaces of multiplicities two and three.
Abstract: We give a negative answer to the embedded Zariski multiplicity conjecture. We construct two reduced hypersurface germs that are ambiently homeomorphic but have multiplicities two and three. Both have isolated singularities and lie in a common complex affine space of dimension divisible by eight. Their defining function germs are also topologically right equivalent, and the same examples answer Arnold's corank problem negatively for ambient topological equivalence.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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