The moduli space of genus $8$ Fano $3$-folds with two $\frac{1}{2}(1,1,1)$-points is rational

TL;DR

This paper proves that the moduli space of genus 8 Fano 3-folds with two specific singularities is a rational variety, providing new insights into their geometric structure.

Contribution

It establishes the rationality of the moduli space of genus 8 Fano 3-folds with two rac{1}{2}(1,1,1) points, a previously unknown result.

Findings

The moduli space al{F}_{8,2rac{1}{2}(1,1,1)} is rational.

The structure of genus 8 Fano 3-folds with two rac{1}{2}(1,1,1) points is explicitly characterized.

The result advances understanding of the birational geometry of Fano 3-folds.

Abstract

Let $\mathcal{F}_{8,2\times \frac{1}{2}(1,1,1)}$ be the moduli space of genus $8$ Fano $3$-folds with two singular points of type $\frac{1}{2}(1,1,1)$. We show that $\mathcal{F}_{8,2\times \frac{1}{2}(1,1,1)}$ is a rational variety.