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Journals / Fundamental Journal of Mathematics and Applications / 2026 / Volume: 5 Issue: 3

The Finiteness of Smooth Curves of Degree $\le 11$ and Genus $\le 3$ on a General Complete Intersection of a Quadric and a Quartic in $\mathbb{P}^5$

Edoardo Ballico(University of Trento)0000-0002-1432-7413
Pages
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Publication Date
2022-09-23
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

In this paper, we prove that $W$ contains only finitely many smooth curves $C\subset \mathbb{P}^5$ such that $d:= \deg ({C}) \le 11$, $g:= p_a({C}) \le 3$ and $h^1(\mathcal{O} _C(1)) =0$.

📌 3 Key Takeaways

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Objective & Hypothesis:Let $W\subset \mathbb{P}^5$ be a general complete intersection of a quadric hypersurface and a quartic hypersurface.
📊
Key Findings & Data:Let $W\subset \mathbb{P}^5$ be a general complete intersection of a quadric hypersurface and a quartic hypersurface.
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Conclusion & Impact:In this paper, we prove that $W$ contains only finitely many smooth curves $C\subset \mathbb{P}^5$ such that $d:= \deg ({C}) \le 11$, $g:= p_a({C}) \le 3$ and $h^1(\mathcal{O} _C(1)) =0$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Calabi-Yau threefold · Curves · Curves in a Calabi-Yau threefold

Abstract

Let $W\subset \mathbb{P}^5$ be a general complete intersection of a quadric hypersurface and a quartic hypersurface. In this paper, we prove that $W$ contains only finitely many smooth curves $C\subset \mathbb{P}^5$ such that $d:= \deg ({C}) \le 11$, $g:= p_a({C}) \le 3$ and $h^1(\mathcal{O} _C(1)) =0$.

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Cite This Article

Ballico, E. (2022). The Finiteness of Smooth Curves of Degree $\le 11$ and Genus $\le 3$ on a General Complete Intersection of a Quadric and a Quartic in $\mathbb{P}^5$. Fundamental Journal of Mathematics and Applications, Volume: 5 Issue: 3. https://doi.org/10.33401/fujma.1069957

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