19 research outputs found
Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities
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.Comment: 13 page
Quasihomogeneity of isolated singularities and logarithmic cohomology
We characterize quasihomogeneity of isolated singularities by the injectivity
of the map induced by the first differential of the logarithmic differential
complex in the top local cohomology supported in the singular point.Comment: 5 page