The Automorphism Group of Linear Sections of the Grassmannians G(1,N)

The Grassmannians of lines in projective N-space, G(1,N), are embedded by way of the Pl"ucker embedding in the projective space P(\bigwedge^2 C^{N+1}). Let H^l be a general l-codimensional linear subspace in this projective space. We examine the geometry of the linear sections G(1,N)\cap H^l by studying their automorphism groups and list those which are homogeneous or quasihomogeneous.