Dual embeddings of dense near polygons

Let e: S -> Sigma be a full polarized projective embedding of a dense near polygon S, i.e., for every point p of S, the set H(p) of points at non-maximal distance from p is mapped by e into a hyperplane Pi(p) of Sigma. We show that if every line of S is incident with precisely three points or if S satisfies a certain property (P(de)) then the map p bar right arrow Pi p defines a full polarized embedding e* (the so-called dual embedding of e) of S into a subspace of the dual Sigma* of Sigma. This generalizes a result of [6] where it was shown that every embedding of a thick dual polar space has a dual embedding. We determine which known dense near polygons satisfy property (P(de)). This allows us to conclude that every full polarized embedding of a known dense near polygon has a dual embedding.

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