Schubert varieties and the fusion products. The general case

This paper generalizes the results of the paper \cite{mi3} to the case of the general ${\mathfrak{s}\mathfrak{l}}_2$ Schubert varieties. We study the homomorphisms between different Schubert varieties, describe their geometry and the group of the line bundles. We also derive some consequences, concerning the infinite-dimensional generalized affine grassmanians.