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Finite semifields with a large nucleus and higher secant varieties to Segre varieties

Michel Lavrauw (UGent)
(2011) ADVANCES IN GEOMETRY. 11(3). p.399-410
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Abstract
In [2] a geometric construction was given of a finite semifield from a certain configuration of two subspaces with respect to a Desarguesian spread in a finite-dimensional vector space over a finite field. Moreover, it was proved that any finite semifield can be obtained in this way. In [7] we proved that the configuration needed for the geometric construction given in [2] for finite semifields is equivalent with an (n - 1)-dimensional subspace skew to a determinantal hypersurface in PG (n(2) - 1, q), and provided an answer to the isotopism problem in [2]. In this paper we give a generalisation of the BEL-construction using linear sets, and then concentrate on this configuration and the isotopism problem for semifields with nuclei that are larger than its centre.
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F-Q

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MLA
Lavrauw, Michel. “Finite Semifields with a Large Nucleus and Higher Secant Varieties to Segre Varieties.” ADVANCES IN GEOMETRY 11.3 (2011): 399–410. Print.
APA
Lavrauw, M. (2011). Finite semifields with a large nucleus and higher secant varieties to Segre varieties. ADVANCES IN GEOMETRY, 11(3), 399–410.
Chicago author-date
Lavrauw, Michel. 2011. “Finite Semifields with a Large Nucleus and Higher Secant Varieties to Segre Varieties.” Advances in Geometry 11 (3): 399–410.
Chicago author-date (all authors)
Lavrauw, Michel. 2011. “Finite Semifields with a Large Nucleus and Higher Secant Varieties to Segre Varieties.” Advances in Geometry 11 (3): 399–410.
Vancouver
1.
Lavrauw M. Finite semifields with a large nucleus and higher secant varieties to Segre varieties. ADVANCES IN GEOMETRY. 2011;11(3):399–410.
IEEE
[1]
M. Lavrauw, “Finite semifields with a large nucleus and higher secant varieties to Segre varieties,” ADVANCES IN GEOMETRY, vol. 11, no. 3, pp. 399–410, 2011.
@article{2152980,
  abstract     = {{In [2] a geometric construction was given of a finite semifield from a certain configuration of two subspaces with respect to a Desarguesian spread in a finite-dimensional vector space over a finite field. Moreover, it was proved that any finite semifield can be obtained in this way. In [7] we proved that the configuration needed for the geometric construction given in [2] for finite semifields is equivalent with an (n - 1)-dimensional subspace skew to a determinantal hypersurface in PG (n(2) - 1, q), and provided an answer to the isotopism problem in [2]. In this paper we give a generalisation of the BEL-construction using linear sets, and then concentrate on this configuration and the isotopism problem for semifields with nuclei that are larger than its centre.}},
  author       = {{Lavrauw, Michel}},
  issn         = {{1615-715X}},
  journal      = {{ADVANCES IN GEOMETRY}},
  keywords     = {{F-Q}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{399--410}},
  title        = {{Finite semifields with a large nucleus and higher secant varieties to Segre varieties}},
  url          = {{http://dx.doi.org/10.1515/ADVGEOM.2011.014}},
  volume       = {{11}},
  year         = {{2011}},
}

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