Sets in a finite plane with few intersection numbers and a distinguished point

J. W P Hirschfeld, T. Szonyi

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

There have been many characterizations of the classical curves in PG(2, q) given by the zeros of quadratic and Hermitian forms. The next step is to characterize pencils of such curves. Here it is done in the case that the pencils have a single base point. A key result that emerges from the investigation is that a certain nonclassical unital is simply the union of conics with a common point.

Original languageEnglish
Pages (from-to)229-242
Number of pages14
JournalDiscrete Mathematics
Volume97
Issue number1-3
DOIs
Publication statusPublished - Dec 10 1991

Fingerprint

Intersection number
Pencil of curves
Hermitian form
Unital
Quadratic form
Union
Curve
Zero

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Sets in a finite plane with few intersection numbers and a distinguished point. / Hirschfeld, J. W P; Szonyi, T.

In: Discrete Mathematics, Vol. 97, No. 1-3, 10.12.1991, p. 229-242.

Research output: Contribution to journalArticle

@article{a519c5b4eda24b1b8bf1ed2b6f715fcf,
title = "Sets in a finite plane with few intersection numbers and a distinguished point",
abstract = "There have been many characterizations of the classical curves in PG(2, q) given by the zeros of quadratic and Hermitian forms. The next step is to characterize pencils of such curves. Here it is done in the case that the pencils have a single base point. A key result that emerges from the investigation is that a certain nonclassical unital is simply the union of conics with a common point.",
author = "Hirschfeld, {J. W P} and T. Szonyi",
year = "1991",
month = "12",
day = "10",
doi = "10.1016/0012-365X(91)90439-9",
language = "English",
volume = "97",
pages = "229--242",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "1-3",

}

TY - JOUR

T1 - Sets in a finite plane with few intersection numbers and a distinguished point

AU - Hirschfeld, J. W P

AU - Szonyi, T.

PY - 1991/12/10

Y1 - 1991/12/10

N2 - There have been many characterizations of the classical curves in PG(2, q) given by the zeros of quadratic and Hermitian forms. The next step is to characterize pencils of such curves. Here it is done in the case that the pencils have a single base point. A key result that emerges from the investigation is that a certain nonclassical unital is simply the union of conics with a common point.

AB - There have been many characterizations of the classical curves in PG(2, q) given by the zeros of quadratic and Hermitian forms. The next step is to characterize pencils of such curves. Here it is done in the case that the pencils have a single base point. A key result that emerges from the investigation is that a certain nonclassical unital is simply the union of conics with a common point.

UR - http://www.scopus.com/inward/record.url?scp=0007009239&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0007009239&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(91)90439-9

DO - 10.1016/0012-365X(91)90439-9

M3 - Article

VL - 97

SP - 229

EP - 242

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -