A geometric proof of the upper bound on the size of partial spreads in $H(4n+1,$q2$)$

Frédéric Vanhove

doi:10.3934/amc.2011.5.157

Article Contents

2011, Volume 5, Issue 2: 157-160. Doi: 10.3934/amc.2011.5.157

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A geometric proof of the upper bound on the size of partial spreads in $H(4n+1,$q²$)$

Frédéric Vanhove^1,

1.
Department of Mathematics, Ghent University, Krijgslaan 281, S22, B-9000 Ghent

Received: February 28, 2010

Revised: July 31, 2010

Published: April 2011

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Abstract

We give a geometric proof of the upper bound of q²ⁿ⁺¹$+1$ on the size of partial spreads in the polar space $H(4n+1,$q²$)$. This bound is tight and has already been proved in an algebraic way. Our alternative proof also yields a characterization of the partial spreads of maximum size in $H(4n+1,$q²$)$.

Keywords:

Hermitian varieties,
partial spreads.

Mathematics Subject Classification: 05B25, 51E23.

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References

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