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In this paper, an approach for semantic composition based on space projection operations over basic geometric lexical representations is proposed. Syntactic bi-grams are here projected in the so called Support Subspace, aimed at emphasizing the semantic features shared by the compound word. Empirical results are discussed over two tasks: a fine grained similarity estimation task over syntactically typed word 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.