Counting lines on surfaces, especially quintics

authored by

Sławomir Rams, Matthias Schütt

Abstract

We introduce certain rational functions on a smooth projective surface X in IP^3 which facilitate counting the lines on X. We apply this to smooth quintics in characteristic zero to prove that they contain no more than 127 lines, and that any given line meets at most 28 others. We construct examples which demonstrate that the latter bound is sharp.

Organisation(s)

Institut für Algebraische Geometrie
Riemann Center for Geometry and Physics

External Organisation(s)

Jagiellonian University

Type

Artikel

Journal

Annali della Scuola Normale - Classe di Scienze

Volume

20

Pages

859-890

No. of pages

32

ISSN

0391-173X

Publication date

11.09.2020

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Mathematik (insg.)

Electronic version(s)

https://arxiv.org/abs/1803.03548 (Access: Offen)
https://doi.org/10.2422/2036-2145.201804_024 (Access: Geschlossen)