Examples
- In PG(d,q), with d odd and d ≥ 3, the set of all points, with as subspaces the totally isotropic subspaces of an arbitrary symplectic polarity, forms a polar space of rank (d+1)/2.
- Let Q be a nonsingular quadric in PG(n,q) with character ω. Then the index of Q will be g = (n+w−3)/2. The set of all points on the quadric, together with the subspaces on the quadric, forms a polar space of rank g+1.
- Let H be a nonsingular Hermitian variety in PG(n,q2). The index of H will be . The points on H, together with the subspaces on it, form a polar space of rank .
Read more about this topic: Polar Space
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