On the Hilbert scheme of smooth curves of degree $d=15$ in $\mathbb{P}^5$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909328050487296 |
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| author | Ballico, Edoardo Keem, Changho |
| author_facet | Ballico, Edoardo 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 $\mathcal{H}_{15,g,5}$ for every possible genus $g$ and determine when it is irreducible. We also study the moduli map $\mathcal{H}_{15,g,5}\rightarrow\mathcal{M}_g$ and several key properties such as gonality of a general element as well as characterizing smooth elements of each component. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_00682 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Hilbert scheme of smooth curves of degree $d=15$ in $\mathbb{P}^5$ Ballico, Edoardo Keem, Changho Algebraic Geometry Primary 14C05, Secondary 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 $\mathcal{H}_{15,g,5}$ for every possible genus $g$ and determine when it is irreducible. We also study the moduli map $\mathcal{H}_{15,g,5}\rightarrow\mathcal{M}_g$ and several key properties such as gonality of a general element as well as characterizing smooth elements of each component. |
| title | On the Hilbert scheme of smooth curves of degree $d=15$ in $\mathbb{P}^5$ |
| topic | Algebraic Geometry Primary 14C05, Secondary 14H10 |
| url | https://arxiv.org/abs/2310.00682 |