Kyeong-Dong Park
Research Subjects
Kyeong-Dong Park has a total of 5 co-authors. Here are the top co-authors by number of shared publications:
- Eunjeong Lee
Center for Geometry and Physics, Institute for Basic Science, Pohang, Republic of Korea
1 shared publication - Shin-Young Kim
Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang, Korea
1 shared publication - Shin-Young Kim
Korea Institute for Advanced Study, Dongdaemun-gu, Korea
1 shared publication - Yoosik Kim
Department of Mathematics Department of Mathematics and Statistics Department of Mathematics and Statistics Yonsei University Boston University Boston University
1 shared publication - Yunhyung Cho
Department of Mathematics Education, Sungkyunkwan University, Seoul, Republic of Korea
1 shared publication
Latest Publications
- Open Access
On the deformation rigidity of smooth projective symmetric varieties with Picard number one
Symmetric varieties are normal equivariant open embeddings of symmetric homogeneous spaces and they are interesting examples of spherical varieties. The principal goal of this article is to study the rigidity under K\"{a}hler deformations of smooth projective symmetric varieties with Picard number one.
Open AccessOn the deformation rigidity of smooth projective symmetric varieties with Picard number one
Symmetric varieties are normal equivariant open embeddings of symmetric homogeneous spaces and they are interesting examples of spherical varieties. The principal goal of this article is to study the rigidity under K\"{a}hler deformations of smooth projective symmetric varieties with Picard number one.
- Open Access
On the combinatorics of string polytopes
For a reduced word ${\bf i}$ of the longest element in the Weyl group of $\mathrm{SL}_{n+1}(\mathbb{C})$, one can associate the string cone $C_{\bf i}$ which parametrizes the dual canonical bases. In this paper, we classify all ${\bf i}$'s such that $C_{\bf i}$ is simplicial. We also prove that for any regular dominant weight $\lambda$ of $\mathfrak{sl}_{n+1}(\mathbb{C})$, the corresponding string polytope $\Delta_{\bf i}(\lambda)$ is unimodularly equivalent to the Gelfand-Cetlin polytope associated to $\lambda$ if and only if $C_{\bf i}$ is simplicial. Thus we completely characterize Gelfand-Cetlin type string polytopes in terms of ${\bf i}$.Open AccessOn the combinatorics of string polytopes
For a reduced word ${\bf i}$ of the longest element in the Weyl group of $\mathrm{SL}_{n+1}(\mathbb{C})$, one can associate the string cone $C_{\bf i}$ which parametrizes the dual canonical bases. In this paper, we classify all ${\bf i}$'s such that $C_{\bf i}$ is simplicial. We also prove that for any regular dominant weight $\lambda$ of $\mathfrak{sl}_{n+1}(\mathbb{C})$, the corresponding string polytope $\Delta_{\bf i}(\lambda)$ is unimodularly equivalent to the Gelfand-Cetlin polytope associated to $\lambda$ if and only if $C_{\bf i}$ is simplicial. Thus we completely characterize Gelfand-Cetlin type string polytopes in terms of ${\bf i}$. - Open Access
Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1
Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians and in the 20-dimensional $F_4$-homogeneous manifold associated to a short simple root.
Open AccessStandard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1
Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians and in the 20-dimensional $F_4$-homogeneous manifold associated to a short simple root.