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arXiv · 2512.06670

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

Kiryong Chung·Bomyeong Kim·Minseong Kwon
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Abstract

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 $\mathrm{Gr}(2,5)$. In this paper, we prove that the Hilbert scheme of conics in $X$ is a smooth variety of dimension $7$ by using a torus action on $X$, which provides a more direct proof about the first named author's previous result.

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Kiryong Chung, Bomyeong Kim, Minseong Kwon. 2025-12-26. Local structure of the Hilbert scheme of conics in quintic del Pezzo varieties. https://arxiv.org/abs/2512.06670

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