Isolated hypersurface singularities and special polynomial realizations of affine quadrics

G. Fels; A. Isaev; W. Kaup; N. Kruzhilin

doi:10.1007/s12220-011-9223-y

Isolated hypersurface singularities and special polynomial realizations of affine quadrics

G. Fels^*, A. Isaev, W. Kaup, N. Kruzhilin

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	767-782
Number of pages	16
Journal	Journal of Geometric Analysis
Volume	21
Issue number	3
DOIs	https://doi.org/10.1007/s12220-011-9223-y
Publication status	Published - Jul 2011

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title = "Isolated hypersurface singularities and special polynomial realizations of affine quadrics",

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

keywords = "Gorenstein algebras, Isolated hypersurface singularities",

author = "G. Fels and A. Isaev and W. Kaup and N. Kruzhilin",

year = "2011",

month = jul,

doi = "10.1007/s12220-011-9223-y",

language = "English",

volume = "21",

pages = "767--782",

journal = "Journal of Geometric Analysis",

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T1 - Isolated hypersurface singularities and special polynomial realizations of affine quadrics

AU - Fels, G.

AU - Isaev, A.

AU - Kaup, W.

AU - Kruzhilin, N.

PY - 2011/7

Y1 - 2011/7

N2 - Let V , Ṽ be hypersurface germs in Cm, each having a quasi-homogeneous isolated singularity at the origin. We show that the biholomorphic equivalence problem for V , Ṽ reduces to the linear equivalence problem for certain polynomials P, P̃ arising from the moduli algebras of V , Ṽ . The polynomials P, P̃ are completely determined by their quadratic and cubic terms, hence the biholomorphic equivalence problem for V , Ṽ in fact reduces to the linear equivalence problem for pairs of quadratic and cubic forms.

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

KW - Gorenstein algebras

KW - Isolated hypersurface singularities

UR - https://www.scopus.com/pages/publications/80051802290

U2 - 10.1007/s12220-011-9223-y

DO - 10.1007/s12220-011-9223-y

M3 - Article

SN - 1050-6926

VL - 21

SP - 767

EP - 782

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 3

ER -

Isolated hypersurface singularities and special polynomial realizations of affine quadrics

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