2022/07/03 by Ceria, Michela, Pavese, Francesco
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2207.01128
In this paper we are concerned with m-ovoids of the symplectic polar space \cal W(2n+1, q), q even. In particular we show the existence of an elliptic quadric of \rm PG(2n+1, q) not polarizing to \cal W(2n+1, q) forming a ((qn-1)/(q-1))-ovoid of \cal W(2n+1, q). A further class of (q+1)-ovoids of \cal W(5, q) is exhibited. It arises by glueing together two orbits of a subgroup of \rm PSp(6, q) isomorphic to \rm PSL(2, q2). We also show that the obtained m-ovoids do not fall in any of the examples known so far in the literature. Moreover, a computer classification of the m-ovoids of \cal W(5, 2) is acquired. It turns out that \cal W(5, 2) has m-ovoids if and only if m = 3 and that there are exactly three pairwise non-isomorphic examples. The first example comes from an elliptic quadric \cal Q-(5, 2) polarizing to \cal W(5, 2), whereas the other two are the 3-ovoids previously mentioned.