Buildings are combinatorial constructions successfully exploited to study groups of various
types. The vertex set of a building can be naturally decomposed into subsets called …

Given a (thick) irreducible spherical building Ω, we establish a bound on the difference
between the generating rank and the embedding rank of its long root geometry and the …

We investigate the possible ways in which a thick metasymplectic space Γ, that is, a Lie
incidence geometry of type F4, 1 (or F4, 4), is embedded into the long root geometry∆ …

Given a non-singular quadratic form q of maximal Witt index on V:=V(2n+1,F), let Δ be the
building of type B n formed by the subspaces of V totally singular for q and, for 1≤ k≤ n, let …

Suppose 𝕆 is an alternative division algebra that is quadratic over some subfield 𝕂 of its
center Z (𝕆). Then with (𝕆, 𝕂), there is associated a dual polar space. We provide an explicit …

On the generation of polar grassmannians Page 345 7 On the Generation of Polar
Grassmannians Ilaria Cardinali, Luca Giuzzi and Antonio Pasini Abstract In this chapter we …

We prove that the Grassmannian of totally isotropic k-spaces of the polar space associated
to the unitary group SU2n (F)(n∈ N) has generating rank (2nk) when F≠ F4. We also …

In this paper we compute the generating rank of k-polar Grassmannians defined over
commutative division rings. Among the new results, we compute the generating rank of k …

Polarized and homogeneous embeddings of dual polar spaces Page 1 J Algebr Comb (2009)
30: 381–399 DOI 10.1007/s10801-008-0166-8 Polarized and homogeneous embeddings of …

We provide a combinatorial characterization of LG (3, 6)() using an axiom set which is the
natural continuation of the Mazzocca–Melone set we used to characterize Severi varieties …