Projections of Veronese surface and Morphisms from projective plane to   Grassmannian
  In this note we describe the image of $\PP^2$ in $ Gr(2, \CC^{4})$ under a morphism given by a rank two vector bundle on $\PP^2$ with Chern classes $(2,2).$ 
A. El Mazouni, F. Laytimi and D.S. Nagaraj
math.AG