Kuga-Satake construction on families of K3 surfaces of Picard rank 14
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_ | 1866912320746160128 |
|---|---|
| author | Poon, Flora |
| author_facet | Poon, Flora |
| contents | The isometry between the type IV$_6$ and the type II$_4$ hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank $14$ and of polarised abelian $8$-folds with totally definite quaternion multiplication. We show how this isometry induces a geometrically meaningful map between such moduli spaces using the Kuga-Satake construction. Furthermore, we illustrate how the the modular mapping can be realised for any specific families of K3 surfaces of Picard rank $14$, which can be specialised to families of K3 surfaces of higher Picard rank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08270 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kuga-Satake construction on families of K3 surfaces of Picard rank 14 Poon, Flora Algebraic Geometry 14J28, 14K10, 14D22 The isometry between the type IV$_6$ and the type II$_4$ hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank $14$ and of polarised abelian $8$-folds with totally definite quaternion multiplication. We show how this isometry induces a geometrically meaningful map between such moduli spaces using the Kuga-Satake construction. Furthermore, we illustrate how the the modular mapping can be realised for any specific families of K3 surfaces of Picard rank $14$, which can be specialised to families of K3 surfaces of higher Picard rank. |
| title | Kuga-Satake construction on families of K3 surfaces of Picard rank 14 |
| topic | Algebraic Geometry 14J28, 14K10, 14D22 |
| url | https://arxiv.org/abs/2504.08270 |