Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities

2014/02/25 by M. G. Eastwood, Eastwood, M. G., A. V. Isaev +1
Mathematics · #13A50 #32S25 #Commutative Algebra (math.AC) #Complex Variables (math.CV) #FOS: Mathematics #Primary 13H10 #Secondary 13E10 #math.AC #math.CV #msc:13A50 #msc:13E10 #msc:13H10 #msc:32S25

paper · pdf · doi:10.48550/arxiv.1402.6049

13 pages

arxiv created 2014/02/25 · arxiv updated 2014/02/26

Abstract

We survey our recently proposed method for constructing biholomorphic invariants of quasihomogeneous isolated hypersurface singularities and, more generally, invariants of graded Artinian Gorenstein algebras. The method utilizes certain polynomials associated to such algebras, called nil-polynomials, and we compare them with two other classes of polynomials that have also been used to produce invariants.

Related

• Extracting Invariants of Isolated Hypersurface Singularities from their Moduli Algebras
• Nilpotent algebras and affinely homogeneous surfaces
• On the Affine Homogeneity of Algebraic Hypersurfaces Arising from Gorenstein Algebras
• Continuous Invariants of Isolated Hypersurface Singularities
• Quasihomogeneous isolated singularities in terms of syzygies and foliations