Let q > 2·34t be even. We prove that the only symplectic semifield spread of PG(5, qt), whose associate semifield has center containing Fq, is the Desarguesian spread. Equivalently, a commutative semifield of order q3t, with middle nucleus containing Fqt and center containing Fq, is a field. We do that by proving that the only possible Fq-linear set of rank 3t in PG(5, qt) disjoint from the secant variety of the Veronese surface is a plane of PG(5, qt).
Symplectic semifield spreads of PG(5, qt), q even / Pepe, Valentina. - In: ARS MATHEMATICA CONTEMPORANEA. - ISSN 1855-3966. - 17:2(2019), pp. 515-524. [10.26493/1855-3974.1763.6cb]
Symplectic semifield spreads of PG(5, qt), q even
Pepe Valentina
2019
Abstract
Let q > 2·34t be even. We prove that the only symplectic semifield spread of PG(5, qt), whose associate semifield has center containing Fq, is the Desarguesian spread. Equivalently, a commutative semifield of order q3t, with middle nucleus containing Fqt and center containing Fq, is a field. We do that by proving that the only possible Fq-linear set of rank 3t in PG(5, qt) disjoint from the secant variety of the Veronese surface is a plane of PG(5, qt).| File | Dimensione | Formato | |
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