Legendrian varieties

2004/07/15 by J. M. Landsberg, Landsberg, J. M., L. Manivel +1 · 1 citation
Mathematics · #14J25 #14J40 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J25 #msc:14J40

paper · pdf · doi:10.48550/arxiv.math/0407279

21 pages

arxiv created 2004/07/15 · arxiv updated 2009/12/01

Abstract

We investigate the geometry of Legendrian complex projective manifolds X⊂\PP V. By definition, this means V is a complex vector space of dimension 2n+2, endowed with a symplectic form, and the affine tangent space to X at each point is a maximal isotropic subspace. We establish basic facts about their geometry and exhibit examples of inhomogeneous smooth Legendrian varieties, the first examples of such in dimension greater than one.

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• Classification of Equivariant Legendrian Embeddings of Rational Homogeneous Spaces into Nilpotent Orbits

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