Zum Aussen- und Innengebiet von Quadriken

Abstract

A point X of a projective space Pⁿ (over a commutative field of characteristic ≠ 2) is called an outer point of a quadric Qⁿ⁻¹ if and only if X is not a point of Qⁿ⁻¹ and the polar hyperplane Γ_X contains a maximal subspace of Qⁿ⁻¹; the points of PⁿQⁿ⁻¹ which are not outer points of Qⁿ⁻¹ are called inner points of Qⁿ⁻¹. This definition is motivated by special cases in classical projective geometry; it improves earlier definitions.