On negative weight derivations of the moduli algebras of weighted homogeneous hypersurface singularities
Let \((V,0) \subseteq (\mathbb{C}^{n + 1}, 0)\) be an isolated singularity defined by a quasihomogeneous polynomial \(f(x_0, x_1, \dots, x_n)\), \(A(V) = C\{x_0, x_1, \dots, x_n\} / (f, {\partial f \over \partial x_0}, {\partial f \over \partial x_1}, \dots, {\partial f \over \partial x_n})\) be its moduli algebra and \(L(V)\) be the Lie algebra of derivations on \(A(V)\). We prove that there is no negative weight derivation in \(L(V)\) in the case of \(n = 3\). Hence a microlocal characterization of quasihomogeneous singularities only using \(L(V)\) of Stephen S. T. Yau can be proved completely in the case of dimension 3.
scientific article; zbMATH DE number 840176