English

Feet in Orthogonal-Buekenhout-Metz Unitals

Combinatorics 2016-04-22 v1

Abstract

Given an Orthogonal-Buekenhout-Metz unital Uα,βU_{\alpha,\beta}, embedded in PG(2,q2)PG(2,q^2), and a point PUα,βP\notin U_{\alpha,\beta}, we study the set of feet, τP(Uα,β)\tau_{P}(U_{\alpha,\beta}), of PP in Uα,βU_{\alpha,\beta}. We characterize geometrically each of these sets as either q+1q+1 collinear points or as q+1q+1 points partitioned into two arcs. Other results about the geometry of these sets are also given.

Keywords

Cite

@article{arxiv.1604.06137,
  title  = {Feet in Orthogonal-Buekenhout-Metz Unitals},
  author = {Nicolas Abarzua and Rolando Pomareda and Oscar Vega},
  journal= {arXiv preprint arXiv:1604.06137},
  year   = {2016}
}

Comments

11 pages, 0 figures