On the degree of irrationality of low genus $K3$ surfaces
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915242139713536 |
|---|---|
| author | Moretti, Federico Rojas, Andrés |
| author_facet | Moretti, Federico Rojas, Andrés |
| contents | Given a general polarized $K3$ surface $S\subset \mathbb P^g$ of genus $g\le 14$, we study projections $S\hookrightarrow \mathbb P^g\dashrightarrow \mathbb P^2$ of minimal degree and their variational structure. In particular, we prove that the degree of irrationality of all such surfaces is at most $4$, and that for $g=7,8,9,11$ there are no rational maps $S\dashrightarrow \mathbb P^2$ of degree $3$ induced by the primitive linear system. Our methods combine vector bundle techniques à la Lazarsfeld with derived category tools, and also make use of the rich theory of singular curves on $K3$ surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03821 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the degree of irrationality of low genus $K3$ surfaces Moretti, Federico Rojas, Andrés Algebraic Geometry 14E05, 14F08, 14J28 Given a general polarized $K3$ surface $S\subset \mathbb P^g$ of genus $g\le 14$, we study projections $S\hookrightarrow \mathbb P^g\dashrightarrow \mathbb P^2$ of minimal degree and their variational structure. In particular, we prove that the degree of irrationality of all such surfaces is at most $4$, and that for $g=7,8,9,11$ there are no rational maps $S\dashrightarrow \mathbb P^2$ of degree $3$ induced by the primitive linear system. Our methods combine vector bundle techniques à la Lazarsfeld with derived category tools, and also make use of the rich theory of singular curves on $K3$ surfaces. |
| title | On the degree of irrationality of low genus $K3$ surfaces |
| topic | Algebraic Geometry 14E05, 14F08, 14J28 |
| url | https://arxiv.org/abs/2401.03821 |