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arXiv · 1504.07845

A non-existence result on symplectic semifield spreads

Stefano Capparelli·Valentina Pepe
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Abstract

We prove that there do not exist non-Desarguesian symplectic semifield spreads of PG$(5,q^2)$, $q\geq 2^{14}$ even, whose associated semifield has center containing $\mathbb{F}_q$, by proving that the only $\mathbb{F}_q$-linear set of rank 6 disjoint from the secant variety of the quadric Veronese variety of PG$(5,q^2)$ is a plane with three points of the Veronese surface of PG$(5,q^6)\setminus$PG$(5,q^2)$.

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Stefano Capparelli, Valentina Pepe. 2015-05-22. A non-existence result on symplectic semifield spreads. https://arxiv.org/abs/1504.07845

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