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arXiv · 2505.09130

Quartic curves in the quintic del Pezzo threefold

Kiryong Chung·Jaehyun Kim·Jeong-Seop Kim
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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 $X_5$.

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Kiryong Chung, Jaehyun Kim, Jeong-Seop Kim. 2025-05-14. Quartic curves in the quintic del Pezzo threefold. https://arxiv.org/abs/2505.09130

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