Lines on K3 quartic surfaces in characteristic 3
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2016
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911828983939072 |
|---|---|
| author | Veniani, Davide Cesare |
| author_facet | Veniani, Davide Cesare |
| contents | We investigate the number of straight lines contained in a K3 quartic surface \(X\) defined over an algebraically closed field of characteristic 3. We prove that if \(X\) contains 112 lines, then \(X\) is projectively equivalent to the Fermat quartic surface; otherwise, \(X\) contains at most 67 lines. We improve this bound to 58 if \(X\) contains a star (ie four distinct lines intersecting at a smooth point of \(X\)). Explicit equations of three 1-dimensional families of smooth quartic surfaces with 58 lines, and of a quartic surface with 8 singular points and 48 lines are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1608_04209 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Lines on K3 quartic surfaces in characteristic 3 Veniani, Davide Cesare Algebraic Geometry 14J28, 14N10, 14N25 We investigate the number of straight lines contained in a K3 quartic surface \(X\) defined over an algebraically closed field of characteristic 3. We prove that if \(X\) contains 112 lines, then \(X\) is projectively equivalent to the Fermat quartic surface; otherwise, \(X\) contains at most 67 lines. We improve this bound to 58 if \(X\) contains a star (ie four distinct lines intersecting at a smooth point of \(X\)). Explicit equations of three 1-dimensional families of smooth quartic surfaces with 58 lines, and of a quartic surface with 8 singular points and 48 lines are provided. |
| title | Lines on K3 quartic surfaces in characteristic 3 |
| topic | Algebraic Geometry 14J28, 14N10, 14N25 |
| url | https://arxiv.org/abs/1608.04209 |