The Non-Existence of 𝔽 Q -Translation Spreads of H ( Q 2 )

Using the connection between translation spreads of the generalized hexagon H ( q ) and linear sets (see Cardinali et al. in Eur J Comb 23:367–376, 2002; Lunardon and Polverino in J Algebraic Comb 18:255–262, 2003), the non-existence of 𝔽 q -translation spreads of H ( q 2 ) when p > 3 , q = p h , and q is large enough is proven. This answers to a question posed in [Marino and Polverino in J Algebraic Comb 42:725-744, 2015].