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Feet in orthogonal-Buekenhout–Metz unitals

  • N. Abarzúa , R. Pomareda and O. Vega EMAIL logo
From the journal Advances in Geometry

Abstract

Given an orthogonal-Buekenhout–Metz unital Uα,β, embedded in PG(2, q2), and a point PUα,β, we study the set τP(Uα,β) of feet of P in Uα,β. We characterize geometrically each of these sets as either q + 1 collinear points or as q + 1 points partitioned into two arcs. Other results about the geometry of these sets are also given.


Communicated by: G. Korchmáros


Acknowledgements

The authors would like to thank Universidad de Chile, and its Stimulus Program for Institutional Excellence for supporting the third author’s visit to Universidad de Chile, where a part of this work was done. Also, the third author would like to thank the California State University Chancellors offices research, scholarship& creative activities award for its support during Fall 2015.

  1. Funding: During the time this project was done, the second author was funded by Fondecyt project # 1140510.

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Received: 2016-4-21
Published Online: 2018-3-26
Published in Print: 2018-4-25

© 2018 Walter de Gruyter GmbH Berlin/Boston

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