- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- Upper bounds on the number of lines on a surface
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
Upper bounds on the number of lines on a surface Elkies, Noam D.
Description
We prove that for q>1 a smooth surface of degree q+1
over any field has at most (q+1)(q^3+1) lines, and thus that
when q is a prime power the "Hermitian" (a.k.a. diagonal) surface
of that degree over a field of q^2 elements has the maximal number
of lines for its degree. This was previously known only for q=3
(Rams-Schuett 2015) and of course q=2. This is one of several cases
where we obtain a sharp bound; other examples are the 126 tritangents
of the Fermat sextic in characteristic 5 (and likewise for other
"Hermitian" curves in odd characteristic), and the 891 planes on
the diagonal cubic fourfold in characteristic 2.
Item Metadata
| Title |
Upper bounds on the number of lines on a surface
|
| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
| Date Issued |
2017-03-15T09:00
|
| Description |
We prove that for q>1 a smooth surface of degree q+1
over any field has at most (q+1)(q^3+1) lines, and thus that
when q is a prime power the "Hermitian" (a.k.a. diagonal) surface
of that degree over a field of q^2 elements has the maximal number
of lines for its degree. This was previously known only for q=3
(Rams-Schuett 2015) and of course q=2. This is one of several cases
where we obtain a sharp bound; other examples are the 126 tritangents
of the Fermat sextic in characteristic 5 (and likewise for other
"Hermitian" curves in odd characteristic), and the 891 planes on
the diagonal cubic fourfold in characteristic 2.
|
| Extent |
61 minutes
|
| Subject | |
| Type | |
| File Format |
video/mp4
|
| Language |
eng
|
| Notes |
Author affiliation: Harvard University
|
| Series | |
| Date Available |
2017-09-11
|
| Provider |
Vancouver : University of British Columbia Library
|
| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
| DOI |
10.14288/1.0355541
|
| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
|
| Scholarly Level |
Faculty
|
| Rights URI | |
| Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International