Classification of n-dimensional subvarieties of G(1, 2n) that can be projected to G(1, n + 1)

Abstract

A structure theorem is given for n-dimensional smooth subvarieties of the Grassmannian G(1, N), with N ≥ n + 3, that can be isomorphically projected to G(1, n + 1). A complete classification in the cases N = 2n + 1 and N = 2n follows, as a corollary