A Weak Fano Threefold Arising as a Blowup of a Curve of Genus 5 and Degree 8 on $\mathbb{P}^3$

TL;DR

This paper constructs a specific weak Fano threefold as a blowup of a genus 5, degree 8 curve in projective 3-space, providing a new explicit construction that simplifies previous approaches.

Contribution

It offers a new explicit construction of a weak Fano threefold arising from a curve of genus 5 and degree 8, removing dependencies on prior complex results.

Findings

Constructed a smooth weak Fano threefold with Picard number two.

Demonstrated the existence of the threefold as a blowup of a specific curve.

Provided a simplified construction method in the style of ACM17.

Abstract

This article constructs a smooth weak Fano threefold of Picard number two with small anti-canonical morphism that arises as a blowup of a smooth curve of genus 5 and degree 8 in $\mathbb{P}^3$. While the existence of this weak Fano was known as a numerical possibility in \cite{CM13} and constructed in BL12, this paper removes the dependencies on the results in \cite{JPR11} needed in the construction of BL12 and constructs the link in the style of ACM17.