In this paper, an approach for semantic compositionbased on space projection operations over basic geometriclexical representations is proposed. Syntactic bi-grams arehere projected in the so called Support Subspace, aimed atemphasizing the semantic features shared by the compoundword. Empirical results are discussed over two tasks: a finegrainedsimilarity estimation task over syntactically typedword pairs and the Semantic Textual Similarity (STS) taskas defined by SemEval 2012. The generalization capabilities ofthe proposed compositional operators are also investigated ina cross-linguistic scenario, i.e. over English and Italian.