Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.06200 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- In our previous research, we constructed the affine varieties $Σ_{\mathbb{A}}^{13}$ and $Π_{\mathbb{A}}^{14}$ whose partial projectivizations admit $\mathbb{P}^{2}\times\mathbb{P}^{2}$-fibrations with relative Picard number one. In this paper, we produce prime quasi-smooth $\mathbb{Q}$-Fano 3-folds which are anticanonically embedded of codimension four and belong to 23 (resp.8) classes in the Graded Ring Database [GRDB], as weighted complete intersections in weighted projectivizations of $Σ_{\mathbb{A}}^{13}$ (resp.$Π_{\mathbb{A}}^{14}$ or its cone). We also show that a general member of the anticanonical linear system of a general prime $\mathbb{Q}$-Fano $3$-fold constructed in this way is a quasi-smooth $K3$ surface with at worst Du Val singularities.