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arXiv · 1007.4356

Isolated hypersurface singularities and polynomial realizations of affine quadrics

G. Fels·A. Isaev·W. Kaup·N. Kruzhilin
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Abstract

Let $V$, $\tilde V$ be hypersurface germs in $\CC^m$, each having a quasi-homogeneous isolated singularity at the origin. We show that the biholomorphic equivalence problem for $V$, $\tilde V$ reduces to the linear equivalence problem for certain polynomials $P$, $\tilde P$ arising from the moduli algebras of $V$, $\tilde V$. The polynomials $P$, $\tilde P$ are completely determined by their quadratic and cubic terms, hence the biholomorphic equivalence problem for $V$, $\tilde V$ in fact reduces to the linear equivalence problem for pairs of quadratic and cubic forms.

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G. Fels, A. Isaev, W. Kaup, N. Kruzhilin. 2010-07-25. Isolated hypersurface singularities and polynomial realizations of affine quadrics. https://arxiv.org/abs/1007.4356

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