Symplectic Spreads and Quadric Veronesean
Guglielmo Lunardon, Giuseppe Marino, Olga Polverino, Rocco Trombetti · 2009
In this paper we face with the problem of constructing semifield spreads in projective spaces of dimension larger than 3. To this aim we study the relationship between linear sets disjoint from the secant variety of a Segre variety Sn,n of PG(n 2 1,q) and semifield spreads of PG(2n 1,q), focusing on the symplectic case. When n = 3, we construct a new symplectic semifield spread of PG(5,q), q odd. Using the cubical array, we describe the associated commutative semifield and deal with the isotopy issue for this example.