SASAKIAN MANIFOLDS, HODGE DECOMPOSITION AND MILNOR ALGEBRAS

Abstract

In this paper we show that Hodge numbers h^p,q of a compact Sasakian (2n + 1)-manifold M, 2n + 1 ≥ 5, are given by the dimension of certain linear subspaces of the Milnor algebras C[z_i]/(∂f/∂z_i), when M is a link of an isolated singularity associated with a weighted homogeneous polynomial f = f(z₁,…,z_n+2).