# Nearly all subspaces of a classical polar space arise from its universal embedding.

@article{Cardinali2020NearlyAS,
title={Nearly all subspaces of a classical polar space arise from its universal embedding.},
author={Ilaria Cardinali and Luca Giuzzi and Antonio Pasini},
journal={arXiv: Representation Theory},
year={2020}
}
• Published 15 October 2020
• Mathematics
• arXiv: Representation Theory
1 Citations
Characterizations of symplectic polar spaces
• Mathematics
• 2022
A polar space S is said to be symplectic if it admits an embedding ε : S → PG( V ) such that the ε -image ε ( S ) of S is deﬁned by an alternating form of V . In this paper we characterize symplectic

## References

SHOWING 1-10 OF 15 REFERENCES
Embedded polar spaces revisited
In this paper we introduce generalized pseudo-quadratic forms and develope some theory for them. Recall that the codomain of a $(\sigma,\varepsilon)$-quadratic form is the group \$\overline{K} :=
Buildings of Spherical Type and Finite BN-Pairs
These notes are a slightly revised and extended version of mim- graphed notes written on the occasion of a seminar on buildings and BN-pairs held at Oberwolfach in April 1968. Their main purpose is
The generating rank of a polar Grassmannian
• Mathematics
• 2021
Abstract 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-Grassmannians
Diagram Geometry
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
Affine polar spaces
• Mathematics
• 1989
Affine polar spaces are polar spaces from which a hyperplane (that is a proper subspace meeting every line of the space) has been removed. These spaces are of interest as they constitute quite
Modern Projective Geometry
• Mathematics
• 2000
Preface. Introduction. 1. Fundamental Notions of Lattice Theory. 2. Projective Geometries and Projective Lattices. 3. Closure Spaces and Matroids. 4. Dimension Theory. 5. Geometries of degree n. 6.
Some Constructions and Embeddings of the Tilde Geometry
• Mathematics
• 2002
Some old and new constructions of the tilde geometry (the flag transitive con- nected triple cover of the unique generalized quadrangle W(2) of order (2, 2)) are discussed. Using them, we prove some
Absolute Embeddings of Point–Line Geometries☆
• Mathematics
• 2001
Abstract A method is given for showing that an embeddable point–line geometry possesses an absolutely universal projective embedding. This method is applied to show that virtually every embeddable
On locally polar geometries whose planes are affine
We give some contributions to the classification of geometries belonging to the following diagram: (Af. Cn)
Points and Lines
“Social convention,” the application of standard terminology to phenomena, is highly influential in science, including archeology. I examine the application of the term “point” to stone and bone