Hilbert scheme of smooth curves of degree sixteen in $\mathbb{P}^5$

Changho Keem

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arXiv · 2503.18428

Hilbert scheme of smooth curves of degree sixteen in $\mathbb{P}^5$

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 study $\mathcal{H}_{16,g,5}$ for almost every possible genus $g$ and chasing after its irreducibility. We also study the natural moduli map $\mathcal{H}_{d,g,5}\stackrel{\mu}{\to}\mathcal{M}_g$ and several key properties such as gonality of a general element as well as characterizing smooth elements in each component.

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Changho Keem. 2025-03-24. Hilbert scheme of smooth curves of degree sixteen in $\mathbb{P}^5$. https://arxiv.org/abs/2503.18428

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