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Semi - Quadratic sets in projective spaces

par Buekenhout, Francis ;Lefèvre, Christiane
Référence Journal of geometry, 7, 1, page (17-42)
Publication Publié, 1976-03

Article révisé par les pairs

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Résumé :

The purpose of this paper is to characterize semi-quadrics in projective spaces P of finite dimension 2 at least. A concept of semi-quadratic set in P is introduced: a semi-quadratic set Q in P is essentially a set of points of P such that the union of all tangent lines at each point p of Q is either a hyperplane of P or P itself. (A tangent line of Q at p is a line contained in Q or meeting Q exactly in p). The main result is that a semi-quadratic set which is invariant under "many" perspectivities is a semi-quadric. © 1976 Birkhäuser Verlag.