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 $\mathbb{P}^5$

Authors : Edoardo Ballico

Pages : 181-191

Doi:10.33401/fujma.1069957

View : 21 | Download : 11

Publication Date : 2022-09-23

Article Type : Research

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