Papers

2025

1. Preprint

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

   Minseong Kwon

   Jul 2025

   Abs arXiv

   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.

2023

1. Preprint

   Spherical Geometry of Hilbert Schemes of Conics in Adjoint Varieties

   Minseong Kwon

   Sep 2023

   Abs arXiv

   For each adjoint variety not of type A or C, we study the irreducible component of the Hilbert scheme which parametrizes all smooth conics. We prove that its normalization is a spherical variety by using contact geometry, and then compute the colored fan of the normalization. As a corollary, we describe the conjugacy classes of conics in the adjoint variety and show smoothness of the normalization. Similar results on the Chow scheme of the adjoint variety are also presented.