Existence and reducibility of the Hilbert scheme of smooth and linearly normal curves in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">P</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msup></mml:math> of relatively high degrees

Keem, Changho

doi:10.1016/j.jpaa.2022.107184

Journal of Pure and Applied Algebra

2023

DOI: 10.1016/j.jpaa.2022.107184

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Existence and reducibility of the Hilbert scheme of smooth and linearly normal curves in Pr of relatively high degrees

Changho Keem

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Cited by 3 publications

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“…This is known only for 𝑟 = 3 by Gruson and Peskine [35,39] and known, except for very large 𝑔, in P 4 and P 5 [64]. Refined versions, prescribing that the curve is linearly normal appear in [49,61,62]. We recall: Theorem 3.…”

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Curves in projective spaces: questions and remarks

Ballico

2022

Proyecciones (Antofagasta)

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confidence: 99%

Curves in projective spaces: questions and remarks

Ballico

2022

Proyecciones (Antofagasta)

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

Ballico,

Keem

2023

Boll Unione Mat Ital

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On the Hilbert scheme of smooth curves of degree d = 15 in $\mathbb{P}^5$

Ballico,

Keem

2024

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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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.

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Existence and reducibility of the Hilbert scheme of smooth and linearly normal curves in Pr of relatively high degrees

Cited by 3 publications

References 25 publications

Curves in projective spaces: questions and remarks

Curves in projective spaces: questions and remarks

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

On the Hilbert scheme of smooth curves of degree d = 15 in $\mathbb{P}^5$

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