|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
On incidences of lines in regular complexes | | Misha Rudnev
; | | Date: |
10 Mar 2020 | | Abstract: | A line complex is a three-parameter set of lines in space, whose Pl"ucker
vectors lie in a hyperplane. The main result is an incidence bound
$O(n^{1/2}m^{3/4} + m+nlog m)$ for the number of incidences between $n$ lines
in a regular complex and $m$ points in $mathbb F^3$, where $mathbb F$ is any
field, with $nleq char(mathbb F)$ in positive characteristic. Zahl has
recently discovered that bichromatic pair-wise incidences of lines coming from
two distinct line complexes describe the nonzero single distance problem for a
set of $n$ points in $mathbb F^3$ and proved a bound $O(n^{3/2})$ for the
number of realisations of the distance, which is a square, for $mathbb F$,
where $-1$ is not a square. Our main theorem entails, under suitable
constraints, a single distance bound $O(n^{1.6})$, which holds for any
distance, including zero over any $mathbb F$ and incidence bound for isotropic
lines in $mathbb F^3$. | | Source: | arXiv, 2003.4744 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER