TY - JOUR
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 - http://www.scopus.com/inward/record.url?scp=80051802290&partnerID=8YFLogxK
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 -