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Characterizations of Hermitian varieties by intersection numbers

Jeroen Schillewaert (UGent) and Joseph Thas (UGent)
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Abstract
In this paper, we give characterizations of the classical generalized quadrangles H(3, q (2)) and H(4, q (2)), embedded in PG(3, q (2)) and PG(4, q (2)), respectively. The intersection numbers with lines and planes characterize H(3, q (2)), and H(4, q (2)) is characterized by its intersection numbers with planes and solids. This result is then extended to characterize all Hermitian varieties in dimension at least 4 by their intersection numbers with planes and solids.
Keywords
1-or-all axiom, Hermitian variety, Intersection number, MULTIPLE BLOCKING SETS, BAER SUBPLANES

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Please use this url to cite or link to this publication:

Chicago
Schillewaert, Jeroen, and Joseph Thas. 2009. “Characterizations of Hermitian Varieties by Intersection Numbers.” Designs Codes and Cryptography 50 (1): 41–60.
APA
Schillewaert, Jeroen, & Thas, J. (2009). Characterizations of Hermitian varieties by intersection numbers. DESIGNS CODES AND CRYPTOGRAPHY, 50(1), 41–60.
Vancouver
1.
Schillewaert J, Thas J. Characterizations of Hermitian varieties by intersection numbers. DESIGNS CODES AND CRYPTOGRAPHY. 2009;50(1):41–60.
MLA
Schillewaert, Jeroen, and Joseph Thas. “Characterizations of Hermitian Varieties by Intersection Numbers.” DESIGNS CODES AND CRYPTOGRAPHY 50.1 (2009): 41–60. Print.
@article{980026,
  abstract     = {In this paper, we give characterizations of the classical generalized quadrangles H(3, q (2)) and H(4, q (2)), embedded in PG(3, q (2)) and PG(4, q (2)), respectively. The intersection numbers with lines and planes characterize H(3, q (2)), and H(4, q (2)) is characterized by its intersection numbers with planes and solids. This result is then extended to characterize all Hermitian varieties in dimension at least 4 by their intersection numbers with planes and solids.},
  author       = {Schillewaert, Jeroen and Thas, Joseph},
  issn         = {0925-1022},
  journal      = {DESIGNS CODES AND CRYPTOGRAPHY},
  language     = {eng},
  number       = {1},
  pages        = {41--60},
  title        = {Characterizations of Hermitian varieties by intersection numbers},
  url          = {http://dx.doi.org/10.1007/s10623-008-9213-7},
  volume       = {50},
  year         = {2009},
}

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