### 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 language | English |
---|---|

Pages (from-to) | 229-242 |

Number of pages | 14 |

Journal | Discrete Mathematics |

Volume | 97 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Dec 10 1991 |

### Fingerprint

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*97*(1-3), 229-242. https://doi.org/10.1016/0012-365X(91)90439-9

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

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 97, no. 1-3, pp. 229-242. https://doi.org/10.1016/0012-365X(91)90439-9

}

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 -