Embedding Theorems for Flexible Varieties

Abstract

Let Z be an affine algebraic variety and X be a smooth flexible variety. We develop some criteria under which Z admits a closed embedding into X. In particular, we show that if $dim\mathit{X}\ge max(2dim\mathit{Z}+1,dim\mathit{T}\mathit{Z})$ and X is isomorphic (as an algebraic variety) to a special linear group or to a symplectic group, then Z admits a closed embedding into X.