On (0,α)(0,α)-sets of generalized quadrangles

Several infinite families of (0,α)(0,α)-sets, α≥1α≥1, of finite classical and non-classical generalized quadrangles are constructed. When α=1α=1 a (0,α)(0,α)-set of a generalized quadrangle is a partial ovoid. We construct a maximal partial ovoid of H(4,q2)H(4,q2), for any q  , of size 2q3+q2+12q3+q2+1, which generalizes the unique largest partial ovoid of H(4,4)H(4,4) of size 21 found in [11], and a maximal partial ovoid of Q−(5,q)Q−(5,q) of size (q+1)2(q+1)2, for any q  . A tight set of a GQ(q−1,q+1)GQ(q−1,q+1) is also provided.