Research field: Algebraic Geometry and Complex Geometry
Professor: Kyeong-Dong Park
Rearch description:
My research interests are focused on the geometry of rational homogeneous varieties and smooth spherical varieties over the field of complex numbers. A normal algebraic G-variety is called spherical if any Borel subgroup of a complex connected reductive group G acts with an open dense orbit. Spherical varieties form a remarkable class of algebraic varieties equipped with an action of an algebraic group. This class contains those of toric varieties, rational homogeneous varieties, horospherical varieties, and symmetric varieties, and is stable under natural operations such as equivariant modifications and degenerations.
To explore the geometry of spherical varieties, I have been studying following topics:
1. Deformation rigidity of complex structures on smooth projective spherical varieties
2. Characterization of standard embeddings of rational homogeneous submanifolds by means of varieties of minimal rational tangents
3. K-stability and Kähler-Einstein metrics of Fano spherical varieties
4. Ulrich vector bundles on smooth spherical varieties and moduli spaces of Ulrich vector bundles on Fano varieties
5. Toric degenerations of spherical varieties via string polytopes and moment polytopes