The Automorphism Group of Linear Sections of the Grassmannians $\GG(1,N)$

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

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

1991 Mathematics Subject Classification: 14L27, 14M15, 14J50, 14E09

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