Factoriality and birational rigidity of two families of singular quartic three-folds
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917357526450176 |
|---|---|
| author | Pukhlikov, Aleksandr V. |
| author_facet | Pukhlikov, Aleksandr V. |
| contents | In this paper we study two families of three-dimensional quartics in the complex projective space ${\mathbb P}^4$: hypersurfaces with a unique quadratic singularity of rank 3, which is resolved by two blowups, and hypersurfaces with two quadratic singularities of rank 3 and 4, respectively. Both families have codimension 3 in the natural parameter space. For a Zariski general quartic in each of these families we prove factoriality and birational rigidity and describe its group of birational self-maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22091 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Factoriality and birational rigidity of two families of singular quartic three-folds Pukhlikov, Aleksandr V. Algebraic Geometry 14E05, 14E07 In this paper we study two families of three-dimensional quartics in the complex projective space ${\mathbb P}^4$: hypersurfaces with a unique quadratic singularity of rank 3, which is resolved by two blowups, and hypersurfaces with two quadratic singularities of rank 3 and 4, respectively. Both families have codimension 3 in the natural parameter space. For a Zariski general quartic in each of these families we prove factoriality and birational rigidity and describe its group of birational self-maps. |
| title | Factoriality and birational rigidity of two families of singular quartic three-folds |
| topic | Algebraic Geometry 14E05, 14E07 |
| url | https://arxiv.org/abs/2512.22091 |