Classification of n ‐Dimensional Subvarieties of G (1, 2 n ) that can be Projected to G (1, n + 1)

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 = 2 n + 1 and N = 2 n follows, as a corollary. 2000 Mathematics Subject Classification 14N15.