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Isolated Hypersurface Singularities and Special Polynomial Realizations of Affine Quadrics

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Abstract

Let V, \(\tilde{V}\) be hypersurface germs in ℂm, 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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Correspondence to A. Isaev.

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Communicated by Steven Krantz.

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Fels, G., Isaev, A., Kaup, W. et al. Isolated Hypersurface Singularities and Special Polynomial Realizations of Affine Quadrics. J Geom Anal 21, 767–782 (2011). https://doi.org/10.1007/s12220-011-9223-y

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  • DOI: https://doi.org/10.1007/s12220-011-9223-y

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