M. Kwon

2026

March

1. Accepted

   Algebraic hyperbolicity of adjoint linear systems on spherical varieties

   Minseong Kwon, and Haesong Seo

   accepted for publication in IMRN, Mar 2026

   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.

2. Math. Z.

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

   Minseong Kwon

   Mathematische Zeitschrift, Mar 2026

   Abs DOI 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.

February

1. Preprint

   Automorphism groups of toroidal horospherical varieties

   Lorenzo Barban, DongSeon Hwang, and Minseong Kwon

   Feb 2026

   Abs arXiv

   We establish a structure theorem for the connected automorphism groups of smooth complete toroidal horospherical varieties, that is, toric fibrations over rational homogeneous spaces. A key ingredient is an extension of the notion of Demazure roots from toric varieties to toroidal horospherical varieties. In particular, we provide a criterion for the reductivity of the connected automorphism groups of such varieties. As an application, we prove the K-unstability of certain P1-bundles over rational homogeneous spaces.