Towards a notion of noncommutative Veronese variety

In recent years, several attempts have been proposed to define a notion of non-commutative toric variety. In this talk, I will report on a work in progress with Francesco Galuppi concerning the definition of a Veronese map between non-commutative algebras. Starting from the definition of the coordinate algebra of the theta-deformed non-commutative projective space, I will describe embeddings of non-commutative projective spaces into the theta-deformed projective line, establishing the necessary conditions for such embeddings to exist and describing the defining ideals for the resulting non-commutative varieties. Finally, I will discuss how this approach relates to existing constructions.