Equivariant Embeddings into Smooth Toric Varieties

http://dx.doi.org/10.4153/CJM-2002-019-0
Canad. J. Math. 54(2002), 554-570

  Published:2002-06-01
 Printed: Jun 2002

We characterize embeddability of algebraic varieties into smooth toric varieties and prevarieties. Our embedding results hold also in an equivariant context and thus generalize a well-known embedding theorem of Sumihiro on quasiprojective $G$-varieties. The main idea is to reduce the embedding problem to the affine case. This is done by constructing equivariant affine conoids, a tool which extends the concept of an equivariant affine cone over a projective $G$-variety to a more general framework.