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 $\mathbb{P}^5$

Year 2022, Volume: 5 Issue: 3, 181 - 191, 23.09.2022

Edoardo Ballico

https://doi.org/10.33401/fujma.1069957

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 $h^1(\mathcal{O} _C(1)) =0$.

Keywords

Calabi-Yau threefold , Curves , Curves in a Calabi-Yau threefold

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