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Dergiler / 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
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Yayın Tarihi
2022-09-23
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

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Amaç & Hipotez:Let $W\subset \mathbb{P}^5$ be a general complete intersection of a quadric hypersurface and a quartic hypersurface.
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Temel Bulgular & Veri:Let $W\subset \mathbb{P}^5$ be a general complete intersection of a quadric hypersurface and a quartic hypersurface.
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Sonuç & Katkı: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 $h^1(\mathcal{O} _C(1)) =0$.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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