Kyeong-Dong Park
Kyeong-Dong Park has a total of 5 co-authors. Here are the top co-authors by number of shared publications:
- Jae-Hyouk Lee
Department of Mathematics, Ewha Womans University 52, Ewhayeodae-gil, Seodaemun-gu, Seoul 03760, Korea
2 shared publications - Kyoung-Seog Lee
Department of Mathematics, POSTECH, Pohang, Korea
2 shared publications - Sungmin Yoo
Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang 37673, Korea
2 shared publications - Eunjeong Lee
Center for Geometry and Physics, Institute for Basic Science, Pohang, Republic of Korea
1 shared publication Kyoung-Seog Lee
Center for Geometry and Physics, Institute for Basic Science (IBS) , Pohang 37673 , Korea
1 shared publication
Latest Publications
- Open Access
Complete intersection hyperkähler fourfolds with respect to equivariant vector bundles over rational homogeneous varieties of Picard number one
We classify fourfolds with trivial canonical bundle which are zero loci of general global sections of completely reducible equivariant vector bundles over exceptional homogeneous varieties of Picard number one. By computing their Hodge numbers, we see that there exist no hyperk\"{a}hler fourfolds among them. This implies that a hyperk\"{a}hler fourfold represented as the zero locus of a general global section of a completely reducible equivariant vector bundle over a rational homogeneous variety of Picard number one is one of the two cases described by Beauville--Donagi and Debarre--Voisin.
Open AccessComplete intersection hyperkähler fourfolds with respect to equivariant vector bundles over rational homogeneous varieties of Picard number one
We classify fourfolds with trivial canonical bundle which are zero loci of general global sections of completely reducible equivariant vector bundles over exceptional homogeneous varieties of Picard number one. By computing their Hodge numbers, we see that there exist no hyperk\"{a}hler fourfolds among them. This implies that a hyperk\"{a}hler fourfold represented as the zero locus of a general global section of a completely reducible equivariant vector bundle over a rational homogeneous variety of Picard number one is one of the two cases described by Beauville--Donagi and Debarre--Voisin.
- Open Access
Equivariant Ulrich bundles on exceptional homogeneous varieties
We prove that the only rational homogeneous varieties with Picard number 1 of the exceptional algebraic groups admitting irreducible equivariant Ulrich vector bundles are the Cayley plane $E_6/P_1$ and the $E_7$-adjoint variety $E_7/P_1$. From this result, we see that a general hyperplane section $F_4/P_4$ of the Cayley plane also has an equivariant but non-irreducible Ulrich bundle.Open AccessEquivariant Ulrich bundles on exceptional homogeneous varieties
We prove that the only rational homogeneous varieties with Picard number 1 of the exceptional algebraic groups admitting irreducible equivariant Ulrich vector bundles are the Cayley plane $E_6/P_1$ and the $E_7$-adjoint variety $E_7/P_1$. From this result, we see that a general hyperplane section $F_4/P_4$ of the Cayley plane also has an equivariant but non-irreducible Ulrich bundle. - 1 April 2021
- Published by Walter de Gruyter GmbH in Advances in Geometry
- Vol. 21 (2) , 187-205
Equivariant Ulrich bundles on exceptional homogeneous varieties
We prove that the only rational homogeneous varieties with Picard number 1 of the exceptional algebraic groups admitting irreducible equivariant Ulrich vector bundles are the Cayley plane E 6/P 1 and the E 7-adjoint variety E 7/P 1. From this result,we see that a general hyperplane section F 4/P 4 of the Cayley plane also has an equivariant but non-irreducible Ulrich bundle.
- 1 April 2021
- Published by Walter de Gruyter GmbH in Advances in Geometry
- Vol. 21 (2) , 187-205
Equivariant Ulrich bundles on exceptional homogeneous varieties
We prove that the only rational homogeneous varieties with Picard number 1 of the exceptional algebraic groups admitting irreducible equivariant Ulrich vector bundles are the Cayley plane E 6/P 1 and the E 7-adjoint variety E 7/P 1. From this result,we see that a general hyperplane section F 4/P 4 of the Cayley plane also has an equivariant but non-irreducible Ulrich bundle.
- Open AccessModuli spaces of Ulrich bundles on the Fano 3-fold $V_5$We study moduli spaces of Ulrich bundles of rank $r \geq 2$ on the Fano 3-fold $V_5$ of Picard number 1, degree 5 and index 2. We prove that the moduli space of stable Ulrich bundles of rank $r$ on $V_5$ can be identified with a smooth $(r^2+1)$-dimensional open subset of the moduli space of stable quiver representations with dimension vector $(r, r)$ of the Kronecker quiver with 2 vertices and 3 arrows.Open AccessModuli spaces of Ulrich bundles on the Fano 3-fold $V_5$We study moduli spaces of Ulrich bundles of rank $r \geq 2$ on the Fano 3-fold $V_5$ of Picard number 1, degree 5 and index 2. We prove that the moduli space of stable Ulrich bundles of rank $r$ on $V_5$ can be identified with a smooth $(r^2+1)$-dimensional open subset of the moduli space of stable quiver representations with dimension vector $(r, r)$ of the Kronecker quiver with 2 vertices and 3 arrows.
- Open Access
Kähler-Einstein metrics on smooth Fano symmetric varieties with Picard number one
Symmetric varieties are normal equivarient open embeddings of symmetric homogeneous spaces, and they are interesting examples of spherical varieties. We prove that all smooth Fano symmetric varieties with Picard number one admit K\"{a}hler-Einstein metrics by using a combinatorial criterion for K-stability of Fano spherical varieties obtained by Delcroix. For this purpose, we present their algebraic moment polytopes and compute the barycenter of each moment polytope with respect to the Duistermaat-Heckman measure.
Open AccessKähler-Einstein metrics on smooth Fano symmetric varieties with Picard number one
Symmetric varieties are normal equivarient open embeddings of symmetric homogeneous spaces, and they are interesting examples of spherical varieties. We prove that all smooth Fano symmetric varieties with Picard number one admit K\"{a}hler-Einstein metrics by using a combinatorial criterion for K-stability of Fano spherical varieties obtained by Delcroix. For this purpose, we present their algebraic moment polytopes and compute the barycenter of each moment polytope with respect to the Duistermaat-Heckman measure.
- Open Access
- 5 January 2021
- Published by MDPI AG in Mathematics
- Vol. 9 (1) , 102
Kähler–Einstein Metrics on Smooth Fano Symmetric Varieties with Picard Number One
Symmetric varieties are normal equivarient open embeddings of symmetric homogeneous spaces, and they are interesting examples of spherical varieties. We prove that all smooth Fano symmetric varieties with Picard number one admit Kähler–Einstein metrics by using a combinatorial criterion for K-stability of Fano spherical varieties obtained by Delcroix. For this purpose, we present their algebraic moment polytopes and compute the barycenter of each moment polytope with respect to the Duistermaat–Heckman measure.
- 5 January 2021
- Published by MDPI AG in Mathematics
- Vol. 9 (1) , 102
Open AccessKähler–Einstein Metrics on Smooth Fano Symmetric Varieties with Picard Number One
Symmetric varieties are normal equivarient open embeddings of symmetric homogeneous spaces, and they are interesting examples of spherical varieties. We prove that all smooth Fano symmetric varieties with Picard number one admit Kähler–Einstein metrics by using a combinatorial criterion for K-stability of Fano spherical varieties obtained by Delcroix. For this purpose, we present their algebraic moment polytopes and compute the barycenter of each moment polytope with respect to the Duistermaat–Heckman measure.