On the Hilbert scheme of smooth curves of degree $15$ and genus $14$ in $\mathbb{P}^5$

Edoardo Ballico; Changho Keem

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arXiv · 2307.14782

On the Hilbert scheme of smooth curves of degree $15$ and genus $14$ in $\mathbb{P}^5$

Edoardo Ballico·Changho Keem

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Abstract

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 show that $\mathcal{H}_{15,14,5}$ is non empty and reducible with two components of the expected dimension hence generically reduced. We also study the birationality of the moduli map up to projective motion and several key properties such as gonality of a general element as well as specifying smooth elements of each components.

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BibTeX RIS

Edoardo Ballico, Changho Keem. 2023-07-27. On the Hilbert scheme of smooth curves of degree $15$ and genus $14$ in $\mathbb{P}^5$. https://arxiv.org/abs/2307.14782

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