Sasakian Manifolds, Hodge Decomposition and Milnor Algebras

Abstract

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 (z 1 , . . . , z n+2 ).