The automorphism group of linear sections of the Grassmannians $\mathbb{G}(1,N)$

Abstract

The Grassmannians of lines in projective $N$-space, $\mathbb{G}(1,N)$, are embedded by way of the Plücker embedding in the projective space $\mathbb{P}({\bigwedge }^2{\mathbb{C}}^{N+1})$. Let $H^l$ be a general $l$-codimensional linear subspace in this projective space.

We examine the geometry of the linear sections $\mathbb{G}(1,N)\cap H^l$ by studying their automorphism groups and list those which are homogeneous or quasihomogeneous.