Antonio Pasini

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The theory of buildings, created by J. Tits three decads ago, has ooered a uniied geometric treatment of nite simple groups of Lie type, both of classical and of exceptional type. (See Tits 19] and 20] for an exposition of that theory; also Ronan 15] and Brown 1].) Diagram geometry (see 13] for an exposition) is a generalization of the theory of buildings.(More)
Let 2 be a finite thick dual polar space of rank 3. We say that a hyperplane H of 2 is locally singular (respectively, quadrangular or ovoidal) if H & Q is the perp of a point (resp. a subquadrangle or an ovoid) of Q for every quad Q of 2. If H is locally singular, quadrangular, or ovoidal, then we say that H is uniform. It is known that if H is locally(More)
Cooperstein [6], [7] proved that every finite symplectic dual polar space DW (2n− 1, q), q 6= 2, can be generated by ( 2n n ) − ( 2n n−2 ) points and that every finite Hermitian dual polar space DH(2n − 1, q2), q 6= 2, can be generated by (2n n ) points. In the present paper, we show that these conclusions remain valid for symplectic and Hermitian dual(More)
The study of geometries on the absolute points of polarities in projective spaces has been started by Veldkamp [21], who was the first to give a synthetic characterization of these geometries, which he called polar spaces. As part of his work on spherical buildings [19], Tits extended Veldkamp’s results to a somewhat larger class of geometries related to(More)
Let be a thick dual polar space of rank n ≥ 2 admitting a full polarized embedding e in a finite-dimensional projective space , i.e., for every point x of , e maps the set of points of at non-maximal distance from x into a hyperplane e∗(x) of . Using a result of Kasikova and Shult [11], we are able the show that there exists up to isomorphisms a unique full(More)
Let ∆ be a dual polar space of rank n ≥ 4, H be a hyperplane of ∆ and Γ := ∆\H be the complement of H in ∆. We shall prove that, if all lines of ∆ have more than 3 points, then Γ is simply connected. Then we show how this theorem can be exploited to prove that certain families of hyperplanes of dual polar spaces, or all hyperplanes of certain dual polar(More)
In [4] we have studied the semibiplanes 6e m,h = A f (S e m,h) obtained as affine expansions of the d-dimensional dual hyperovals of Yoshiara [6]. We continue that investigation here, but from a graph theoretic point of view. Denoting by 0e m,h the incidence graph of (the point-block system of) 6 e m,h , we prove that 0e m,h is distance regular if and only(More)