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

2025/07/05 by Kwon, Minseong
#14M17 #17B08 #53D10 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.03932

Abstract

For a complex semi-simple Lie algebra, every nilpotent orbit in its projectivization comes with a complex contact structure. For each nilpotent orbit, we classify projective Legendrian subvarieties that are homogeneous under the actions of their stabilizers in the adjoint group. In particular, we present a classification of equivariant Legendrian embeddings of rational homogeneous spaces into adjoint varieties.

Citations

• Local geometry of special pieces of nilpotent orbits
• Minimal rational curves on complete symmetric varieties
• Legendrian varieties
• On the projective geometry of homogeneous spaces
• Fano contact manifolds and nilpotent orbits

Related

• Homogeneous spaces and equivariant embeddings
• Characterizing subadjoint varieties among Legendrian varieties
• Generalized Complex and Dirac Structures on Homogeneous Spaces
• Legendrian varieties
• Continuous representations of semisimple Lie groups concerning homogeneous holomorphic vector bundles over elliptic adjoint orbits