Dergiler / Fundamental journal of mathematics and applications (Online) / 2022 / Cilt: 5 - Sayı: 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 $mathbb{P}^5$

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

Sayfa
181–191
DOI
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Abstract

Let $Wsubset mathbb{P}^5$ 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$Csubset mathbb{P}^5$ such that $d:= deg ({C}) le 11$, $g:= p_a({C}) le 3$ and $h^1(mathcal{O} _C(1)) =0$.