Some non-existence results on m-ovoids in classical polar spaces

In this paper we develop non-existence results for m-ovoids in the classical polar spaces Q−(2r+1,q),W(2r−1,q) and H(2r,q2) for r>2. In Bamberg et al. (2009) a lower bound on m for the existence of m-ovoids of H(4,q2) is found by using the connection between m-ovoids, two-character sets, and strongly regular graphs. This approach is generalized in Bamberg et al. (2007) for the polar spaces Q−(2r+1,q),W(2r−1,q) and H(2r,q2), r>2. In Bamberg et al. (2012) an improvement for the particular case H(4,q2) is obtained by exploiting the algebraic structure of the collinearity graph, and using the characterization of an m-ovoid as an intriguing set. In this paper, we use an approach based on geometrical and combinatorial arguments, inspired by the results from Gavrilyuk et al. (2023), to improve the bounds from Bamberg et al. (2007).