Title	Upper bounds on the number of lines on a surface
Creator	Elkies, Noam D.
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	Mathematics; Algebraic geometry; Number theory
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Harvard University
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2017-09-12
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0355541
URI	http://hdl.handle.net/2429/63015
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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