Embedding theorems for quasitoric manifolds

The study of embeddings of smooth manifolds into Euclidean and projective spaces has been for a long time an important area in topology. In this paper we obtain improvements of classical results on embeddings of smooth manifolds, focusing on the case of quasitoric manifolds. We give explicit constructions of equivariant embeddings of a quasitoric manifold described by combinatorial data $(P,\Lambda)$ into Euclidean and complex projective space. This construction provides effective bounds on the dimension of the equivariant embedding.