On some subvarieties of the Grassmann variety

Abstract

Let be a Desarguesian -spread of , a -dimensional subspace of and the linear set consisting of the elements of with non-empty intersection with . It is known that the Plücker embedding of the elements of is a variety of , say . In this paper, we describe the image under the Plücker embedding of the elements of and we show that it is an –dimensional algebraic variety, projection of a Veronese variety of dimension and degree , and it is a suitable linear section of .