Local structure of the Hilbert scheme of conics in quintic del Pezzo varieties
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918263724703744 |
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| author | Chung, Kiryong Kim, Bomyeong Kwon, Minseong |
| author_facet | Chung, Kiryong Kim, Bomyeong Kwon, Minseong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06670 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local structure of the Hilbert scheme of conics in quintic del Pezzo varieties Chung, Kiryong Kim, Bomyeong Kwon, Minseong Algebraic Geometry 14C05, 14H10, 14J45 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. |
| title | Local structure of the Hilbert scheme of conics in quintic del Pezzo varieties |
| topic | Algebraic Geometry 14C05, 14H10, 14J45 |
| url | https://arxiv.org/abs/2512.06670 |