AT MOST 64 LINES ON SMOOTH QUARTIC SURFACES (CHARACTERISTIC 2)
Let $k$ be a field of characteristic $2$ . We give a geometric proof that there are no smooth quartic surfaces $S\subset \mathbb{P}_{k}^{3}$ with more than 64 lines (predating work of Degtyarev which improves this bound to 60). We also exhibit a smooth quartic containing 60 lines which thus attains...
Gespeichert in:
| Veröffentlicht in: | Nagoya mathematical journal 2018-12, Vol.232, p.76-95 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | Let
$k$
be a field of characteristic
$2$
. We give a geometric proof that there are no smooth quartic surfaces
$S\subset \mathbb{P}_{k}^{3}$
with more than 64 lines (predating work of Degtyarev which improves this bound to 60). We also exhibit a smooth quartic containing 60 lines which thus attains the record in characteristic
$2$
. |
|---|---|
| ISSN: | 0027-7630 2152-6842 |
| DOI: | 10.1017/nmj.2017.21 |