#### DOCUMENTA MATHEMATICA, Vol. 4 (1999), 623-664

J. Piontkowski and A. Van de Ven

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

Keywords and Phrases:

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