Explicit reconstruction of homogeneous isolated hypersurface singularities from their Milnor algebras

Details Explicit reconstruction of homogeneous isolated hypersurface singularities from their Milnor algebras Explicit reconstruction of homogeneous isolated hypersurface singularities from their Milnor algebras

2012-03-25

arxiv.org/abs/1203.5549v1

Mathematics

Complex Variables

Scientific paper

By the Mather-Yau theorem, a complex hypersurface germ $V$ with isolated singularity is completely determined by its moduli algebra $A(V)$. The proof of the theorem does not provide an explicit procedure for recovering $V$ from $A(V)$, and finding such a procedure is a long-standing open problem. In this paper, we present an explicit way for reconstructing $V$ from $A(V)$ up to biholomorphic equivalence under the assumption that the singularity of $V$ is homogeneous, in which case $A(V)$ coincides with the Milnor algebra of $V$.

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