Tangency sets in PG(3, q) |
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| Authors: | K Metsch L Storme |
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| Institution: | 1. Mathematisches Institut, Justus‐Liebig‐Universit?t, Arndtstrasse 2, D‐35392 Giessen, Germany;2. Email:ls@cage.ugent.be, http://cage.ugent.be/～ls;5. Ghent University, Department of Pure Mathematics and Computer Algebra, Krijgslaan 281‐S22, 9000 Ghent, Belgium |
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| Abstract: | A tangency set of PG (d,q) is a set Q of points with the property that every point P of Q lies on a hyperplane that meets Q only in P. It is known that a tangency set of PG (3,q) has at most  points with equality only if it is an ovoid. We show that a tangency set of PG (3,q) with  , or  points is contained in an ovoid. This implies the non‐existence of minimal blocking sets of size  ,  , and of  with respect to planes in PG (3,q), and implies the extendability of partial 1‐systems of size  ,  , or  to 1‐systems on the hyperbolic quadric  . © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 462–476, 2008 |
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| Keywords: | tangency sets minimal blocking sets partial 1‐systems |
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