Milnor algebras could be isomorphic to modular algebras

Details Milnor algebras could be isomorphic to modular algebras Milnor algebras could be isomorphic to modular algebras

2007-03-15

arxiv.org/abs/math/0703449v2

Mathematics

Algebraic Geometry

15 pages, 1 table Correction of the proof of lemma/proposition 4.2. Elimination of some inaccuracies and errors in section 5 (

Scientific paper

We find and describe unexpected isomorphisms between two very different objects associated to hypersurface singularities. One object is the Milnor algebra of a function, while the other object associated to a singularity is the local ring of the flatness stratum of the singular locus in a miniversal deformation, an invariant of the contact class of a defining function. Such isomorphisms exist for unimodal hypersurface singularities. However, for the moment it is badly understood, which principle causes these isomorphisms and how far this observation generalises. Here we also provide an algorithmic approach for checking algebra isomorphy.

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