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

1999/04/14 by J. Piontkowski, Piontkowski, J., A. Van de Ven +1
Mathematics · #14E09 #14J50 #14L27 #14M15 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14E09 #msc:14J50 #msc:14L27 #msc:14M15

paper · pdf · doi:10.48550/arxiv.math/9904060

39 pages, 2 figures, e-mail address of the second author is [email protected]

arxiv created 1999/04/14 · arxiv updated 2009/11/30

Abstract

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(\bigwedge² 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)∩ H^l by studying their automorphism groups and list those which are homogeneous or quasihomogeneous.

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