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pro vyhledávání: '"Pasini, Antonio"'
Autor:
Pasini, Antonio
In this paper we propose a definition of regularity suited for polar spaces of infinite rank and we investigate to which extent properties of regular polar spaces of finite rank can be generalized to polar spaces of infinite rank.
Comment: 44 pa
Comment: 44 pa
Externí odkaz:
http://arxiv.org/abs/2307.16293
Autor:
Pasini, Antonio
In this paper we consider a family of projective embeddings of the geometry $\Gamma = A_{n,\{1,n\}}(F)$ of point-hyperplanes flags of the projective geometry $\Sigma = PG(n,F)$. The natural embedding $\varepsilon_{mathrm{nat}}$ is one of them. It map
Externí odkaz:
http://arxiv.org/abs/2306.17079
Autor:
Pasini, Antonio
In this paper we investigate hyperplanes of the point-line geometry $\mathit{A}_{n,\{1,n\}}(\mathbb{F})$ of point-hyerplane flags of the projective geometry $\mathrm{PG}(n,\mathbb{F})$. Renouncing a complete classification, which is not yet within ou
Externí odkaz:
http://arxiv.org/abs/2306.03947
Publikováno v:
Adv. Geom. 23(2) (2023) 281-293
A polar space S is said to be symplectic if it admits an embedding e in a projective geometry PG(V) such that the e-image e(S) of S is defined by an alternating form of V. In this paper we characterize symplectic polar spaces in terms of their incide
Externí odkaz:
http://arxiv.org/abs/2205.14426
Publikováno v:
In Journal of Algebra 15 October 2024 656:367-393
Autor:
Pasini, Antonio
We consider various regular graphs defined on the set of elements of given rank of a finite polar space. It is likely that no two such graphs, of the same kind but defined for different ranks, can have the same degree. We shall prove this conjecture
Externí odkaz:
http://arxiv.org/abs/2105.12616
Publikováno v:
Linar Algebra Appl. 627 (2021), 287-307
Let $\Gamma$ be an embeddable non-degenerate polar space of finite rank $n \geq 2$. Assuming that $\Gamma$ admits the universal embedding (which is true for all embeddable polar spaces except grids of order at least $5$ and certain generalized quadra
Externí odkaz:
http://arxiv.org/abs/2010.07640
Publikováno v:
Journal of Combinatorial Theory, Series A, Volume 193, 2023, 105673
Let $X_n(K)$ be a building of Coxeter type $X_n = A_n$ or $X_n = D_n$ defined over a given division ring $K$ (a field when $X_n = D_n$). For a non-connected set $J$ of nodes of the diagram $X_n$, let $\Gamma(K) = Gr_J(X_n(K))$ be the $J$-Grassmannian
Externí odkaz:
http://arxiv.org/abs/1912.03484
Autor:
Pasini, Antonio
The rank of a point-line geometry G is usually defined as the generating rank of G, namely the minimal cardinality of a generating set. However, when the subspace lattice of G satisfies the Exchange Property we can also try a different definition: co
Externí odkaz:
http://arxiv.org/abs/1910.14660
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 arising from Hermitian forms of Witt index $n$ defined over ve
Externí odkaz:
http://arxiv.org/abs/1906.10560