TH YAU NUMBER of ISOLATED HYPERSURFACE SINGULARITIES and AN INEQUALITY CONJECTURE

Let be a hypersurface with an isolated singularity at the origin defined by the holomorphic function. The Yau algebra is defined to be the Lie algebra of derivations of the moduli algebra, that is,. It is known that is finite dimensional and its dimension is called the Yau number. We introduce a new series of Lie algebras, that is, th Yau algebras, which are a generalization of the Yau algebra. The algebra is defined to be the Lie algebra of derivations of the th moduli algebra, that is, where is the maximal ideal of. The th Yau number is the dimension of, which we denote by. In particular, is exactly the Yau algebra, that is,. These numbers are new numerical analytic invariants of singularities. In this paper we formulate a conjecture that [unicode[STIX]{x1D706}-{k}(V),k 0.]]> We prove this conjecture for a large class of singularities.