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On symplectic semifield spreads of PG(5,q2), q odd

  • Giuseppe Marino und Valentina Pepe EMAIL logo
Veröffentlicht/Copyright: 15. August 2017
Forum Mathematicum
Aus der Zeitschrift Forum Mathematicum Band 30 Heft 2

Abstract

We prove that there exist exactly three non-equivalent symplectic semifield spreads of PG⁡(5,q2), for q2>2⋅38 odd, whose associated semifield has center containing 𝔽q. Equivalently, we classify, up to isotopy, commutative semifields of order q6, for q2>2⋅38 odd, with middle nucleus containing 𝔽q2 and center containing 𝔽q.

Keywords: Commutative semifield; symplectic semifield spread; Veronese variety
MSC 2010: 51A40; 51A50; 12K10; 14M12

Communicated by Jan Bruinier

Funding statement: The first author was supported by Ministry for Education, University and Research of Italy MIUR (Project PRIN 2012 “Geometrie di Galois e strutture di incidenza”) and by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA–INdAM).

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Received: 2016-6-13
Revised: 2017-3-8
Published Online: 2017-8-15
Published in Print: 2018-3-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. The variance of divisor sums in arithmetic progressions
  3. Characterizing Lie groups by controlling their zero-dimensional subgroups
  4. CM cycles on Kuga–Sato varieties over Shimura curves and Selmer groups
  5. Towards a Goldberg–Shahidi pairing for classical groups
  6. On the non-existence of cyclic splitting fields for division algebras
  7. Sequential motion planning algorithms in real projective spaces: An approach to their immersion dimension
  8. Very ampleness of the bicanonical line bundle on compact complex 2-ball quotients
  9. Anharmonic solutions to the Riccati equation and elliptic modular functions
  10. A non-homogeneous local Tb theorem for Littlewood–Paley g*λ-function with Lp-testing condition
  11. Saturation rank for finite group schemes: Finite groups and infinitesimal group schemes
  12. On symplectic semifield spreads of PG(5,q2), q odd
  13. From Freudenthal’s spectral theorem to projectable hulls of unital Archimedean lattice-groups, through compactifications of minimal spectra
  14. Golodness and polyhedral products for two-dimensional simplicial complexes
https://doi.org/10.1515/forum-2016-0133
Schlagwörter für diesen Artikel
Commutative semifield; symplectic semifield spread; Veronese variety

Artikel in diesem Heft

  1. Frontmatter
  2. The variance of divisor sums in arithmetic progressions
  3. Characterizing Lie groups by controlling their zero-dimensional subgroups
  4. CM cycles on Kuga–Sato varieties over Shimura curves and Selmer groups
  5. Towards a Goldberg–Shahidi pairing for classical groups
  6. On the non-existence of cyclic splitting fields for division algebras
  7. Sequential motion planning algorithms in real projective spaces: An approach to their immersion dimension
  8. Very ampleness of the bicanonical line bundle on compact complex 2-ball quotients
  9. Anharmonic solutions to the Riccati equation and elliptic modular functions
  10. A non-homogeneous local Tb theorem for Littlewood–Paley g*λ-function with Lp-testing condition
  11. Saturation rank for finite group schemes: Finite groups and infinitesimal group schemes
  12. On symplectic semifield spreads of PG(5,q2), q odd
  13. From Freudenthal’s spectral theorem to projectable hulls of unital Archimedean lattice-groups, through compactifications of minimal spectra
  14. Golodness and polyhedral products for two-dimensional simplicial complexes
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