M. Kwon

2026

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.

January

1. Accepted

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

   Minseong Kwon

   Jan 2026

   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.

2025

December

1. Preprint

   Local structure of the Hilbert scheme of conics in quintic del Pezzo varieties

   Kiryong Chung, Bomyeong Kim, and Minseong Kwon

   Dec 2025

   Abs arXiv

   Let X be the quintic del Pezzo 4-fold. It is very well-known that X is realized by a smooth linear section of Grassmannian Gr(2,5). In this paper, we prove that the Hilbert scheme of conics in X is a smooth variety of dimension 7 by using a torus action on X, which provides a more direct proof about the first named author’s previous result.