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Quartic curves in the quintic del Pezzo threefold

Year: 2026

Type: article

Abstract: In this paper, we prove that the Hilbert scheme $\mathbf{H}_{4}(X_{5})$ of rational quartic curves on the quintic del Pezzo threefold $X_{5}$ is isomorphic to a Grassmannian bundle over the Hilbert scheme of lines on $X_{5}$. In particular, $\mathbf{H}_{4}(X_{5})$ is smooth and irreducible. Our approach builds upon the geometry of rational quartic curves on $X_{5}$ studied by Fanelli–Gruson–Perrin in their work on the moduli space of stable maps to $X_{5}$.

Source: Journal of the Mathematical Society of Japan

DOI: 10.2969/jmsj/95659565

Authors: Kiryong CHUNG, Jaehyun KIM, Jeong-Seop KIM

Institutions: Kyungpook National University, Kangwon National University, Sunchon National University, National Institute for Mathematical Sciences

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4414938403

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