Hilbert scheme of smooth curves of degree sixteen in $\mathbb{P}^5$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913754175766528 |
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| author | Keem, Changho |
| author_facet | Keem, Changho |
| contents | We denote by $\mathcal{H}_{d,g,r}$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree $d$ and genus $g$ in $\mathbb{P}^r$. In this article, we study $\mathcal{H}_{16,g,5}$ for almost every possible genus $g$ and chasing after its irreducibility. We also study the natural moduli map $\mathcal{H}_{d,g,5}\stackrelμ{\to}\mathcal{M}_g$ and several key properties such as gonality of a general element as well as characterizing smooth elements in each component. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_18428 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hilbert scheme of smooth curves of degree sixteen in $\mathbb{P}^5$ Keem, Changho Algebraic Geometry 14C05, 14H10 We denote by $\mathcal{H}_{d,g,r}$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree $d$ and genus $g$ in $\mathbb{P}^r$. In this article, we study $\mathcal{H}_{16,g,5}$ for almost every possible genus $g$ and chasing after its irreducibility. We also study the natural moduli map $\mathcal{H}_{d,g,5}\stackrelμ{\to}\mathcal{M}_g$ and several key properties such as gonality of a general element as well as characterizing smooth elements in each component. |
| title | Hilbert scheme of smooth curves of degree sixteen in $\mathbb{P}^5$ |
| topic | Algebraic Geometry 14C05, 14H10 |
| url | https://arxiv.org/abs/2503.18428 |