Kiryong Chung

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20232026

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math.AG2026

A remark on rational quartic curves in prime Fano threefolds of degree $22$

Kiryong Chung, Jeong-Seop Kim

In this short note, using the Sarkisov link between a prime Fano threefold $V_{22}$ of degree $22$ and the quintic del Pezzo threefold $V_{5}$ , we prove that the Hilbert scheme of ra…

math.AG2025

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

Kiryong Chung, Bomyeong Kim, Minseong Kwon

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 th…

math.AG2025

Quartic curves in the quintic del Pezzo threefold

Kiryong Chung, Jaehyun Kim, Jeong-Seop Kim

In this paper, we prove that the Hilbert scheme $H_{4} (X_{5})$ of rational quartic curves on the quintic del Pezzo threefold $X_{5}$ is isomorphic to a Grassmannian bundle over…

math.AG2024

Rational quartic curves in the Mukai-Umemura variety

Kiryong Chung, Jaehyun Kim, Jeong-Seop Kim

Let $X$ be the Fano threefold of index one, degree $22$ , and $Pic (X) ≅ Z$ . Such a threefold $X$ can be realized by a regular zero section $s$ of $(\big…

math.AG2023

An $SL (3, C)$ -equivariant smooth compactification of rational quartic plane curves

Kiryong Chung, Jeong-Seop Kim

Let $R_{d}$ be the space of stable sheaves $F$ which satisfy the Hilbert polynomial $χ (F (m)) = d m + 1$ and are supported on rational curves in the projective plane $\mathbb{P}^2…

A remark on rational quartic curves in prime Fano threefolds of degree 22

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

Quartic curves in the quintic del Pezzo threefold

Rational quartic curves in the Mukai-Umemura variety

An SL(3,C)-equivariant smooth compactification of rational quartic plane curves

A remark on rational quartic curves in prime Fano threefolds of degree $22$

An $SL (3, C)$ -equivariant smooth compactification of rational quartic plane curves