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The generating rank of a polar Grassmannian

  • Ilaria Cardinali EMAIL logo , Luca Giuzzi und Antonio Pasini
Veröffentlicht/Copyright: 8. Juli 2021
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Advances in Geometry
Aus der Zeitschrift Advances in Geometry Band 21 Heft 4

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 arising from Hermitian forms of Witt index n defined over vector spaces of dimension N > 2n. We also study generating sets for the 2-Grassmannians arising from quadratic forms of Witt index n defined over V(N, 𝔽q) for q = 4, 8, 9 and 2n ≤ N ≤ 2n + 2. We prove that for N > 6 and anisotropic defect (polar corank) d ≠ 2 they can be generated over the prime subfield, thus determining their generating rank.

Keywords: Polar Grassmannian; generating rank
MSC 2010: 51A50

  1. Communicated by: H. Van Maldeghem

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Received: 2019-06-25
Revised: 2020-05-27
Published Online: 2021-07-08
Published in Print: 2021-10-26

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. An đť”˝p2-maximal Wiman sextic and its automorphisms
  3. Pseudo-algebraic Ricci solitons on Einstein nilradicals
  4. The wobbly divisors of the moduli space of rank-2 vector bundles
  5. Symmetries of complex analytic vector fields with an essential singularity on the Riemann sphere
  6. Betti numbers and pseudoeffective cones in 2-Fano varieties
  7. The generating rank of a polar Grassmannian
  8. The Beckman–Quarles theorem via the triangle inequality
  9. On Huisman’s conjectures about unramified real curves
  10. Geodesic orbit Finsler spaces with K ≥ 0 and the (FP) condition
  11. On the Segre invariant for rank two vector bundles on â„™2
  12. Lifting coarse homotopies
  13. How to construct all metric f-K-contact manifolds
  14. An extremum problem for the power moment of a convex polygon contained in a disc
  15. Sharply transitive sets in PGL2(K)
https://doi.org/10.1515/advgeom-2021-0022
Schlagwörter für diesen Artikel
Polar Grassmannian; generating rank

Artikel in diesem Heft

  1. Frontmatter
  2. An đť”˝p2-maximal Wiman sextic and its automorphisms
  3. Pseudo-algebraic Ricci solitons on Einstein nilradicals
  4. The wobbly divisors of the moduli space of rank-2 vector bundles
  5. Symmetries of complex analytic vector fields with an essential singularity on the Riemann sphere
  6. Betti numbers and pseudoeffective cones in 2-Fano varieties
  7. The generating rank of a polar Grassmannian
  8. The Beckman–Quarles theorem via the triangle inequality
  9. On Huisman’s conjectures about unramified real curves
  10. Geodesic orbit Finsler spaces with K ≥ 0 and the (FP) condition
  11. On the Segre invariant for rank two vector bundles on â„™2
  12. Lifting coarse homotopies
  13. How to construct all metric f-K-contact manifolds
  14. An extremum problem for the power moment of a convex polygon contained in a disc
  15. Sharply transitive sets in PGL2(K)
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