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

TL;DR

This paper investigates the automorphism groups of linear sections of Grassmannians G(1,N), identifying which sections are homogeneous or quasihomogeneous, thereby advancing understanding of their geometric symmetries.

Contribution

It provides a detailed analysis of the automorphism groups of linear sections of G(1,N) and classifies those with homogeneous or quasihomogeneous structures.

Findings

Identified automorphism groups for various linear sections.

Classified sections as homogeneous or quasihomogeneous.

Enhanced understanding of symmetry properties of Grassmannian sections.

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(\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.