Isolated hypersurface singularities and polynomial realizations of affine quadrics

2010/07/25 by Fels, G., Isaev, A., Kaup, W. +1
#16A46 #32S25 #Commutative Algebra (math.AC) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1007.4356

Abstract

Let V, 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, V reduces to the linear equivalence problem for certain polynomials P, P arising from the moduli algebras of V, V. The polynomials P, P are completely determined by their quadratic and cubic terms, hence the biholomorphic equivalence problem for V, V in fact reduces to the linear equivalence problem for pairs of quadratic and cubic forms.

Related

• Extracting Invariants of Isolated Hypersurface Singularities from their Moduli Algebras
• Explicit reconstruction of homogeneous isolated hypersurface singularities from their Milnor algebras
• Quadratic solutions of quadratic forms
• Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities
• Associated Forms and Hypersurface Singularities: The Binary Case