Minseong Kwon

2025

August

1. Preprint

   Algebraic hyperbolicity of adjoint linear systems on spherical varieties

   Minseong Kwon, and Haesong Seo

   Aug 2025

   Abs arXiv

   Moraga and Yeong conjectured that for a smooth complex projective variety X of dimension n, an ample line bundle A on X and an integer m ≥ 3n +1, very general elements of the adjoint linear system ∣ωX ⊗ A⊗m∣ are algebraically hyperbolic. We prove the conjecture for spherical varieties with smooth orbit closures. As a corollary, we conclude that the conjecture holds for horospherical varieties, and for toroidal spherical varieties. Furthermore, for any spherical variety, we show that the conjecture holds modulo the complement of an open dense orbit.

July

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

September

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.