Ricerc@Sapienza

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).