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Slices of the unitary spread

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Abstract
We prove that slices of the unitary spread of Q(+)(7, q), q equivalent to 2 (mod 3), can be partitioned into five disjoint classes. Slices belonging to different classes are non-equivalent under the action of the subgroup of P Gamma O+(8, q) fixing the unitary spread. When q is even, there is a connection between spreads of Q(+)(7, q) and symplectic 2-spreads of PG(5, q) (see Dillon, Ph.D. thesis, 1974 and Dye, Ann. Mat. Pura Appl. (4) 114, 173-194, 1977). As a consequence of the above result we determine all the possible non-equivalent symplectic 2-spreads arising from the unitary spread of Q(+)(7, q), q = 2(2h+1). Some of these already appeared in Kantor, SIAM J. Algebr. Discrete Methods 3(2), 151-165, 1982. When q = 3(h), we classify, up to the action of the stabilizer in P Gamma O(7, q) of the unitary spread of Q(6, q), those among its slices producing spreads of the elliptic quadric Q(-)(5, q).
Keywords
OVOIDS, TRANSLATION-PLANES, Ovoid, Unitary spread, Slice

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MLA
Lunardon, Guglielmo et al. “Slices of the Unitary Spread.” JOURNAL OF ALGEBRAIC COMBINATORICS 33.1 (2011): 37–56. Print.
APA
Lunardon, G., Parlato, L., Pepe, V., & Trombetti, R. (2011). Slices of the unitary spread. JOURNAL OF ALGEBRAIC COMBINATORICS, 33(1), 37–56.
Chicago author-date
Lunardon, Guglielmo, Laura Parlato, Valentina Pepe, and Rocco Trombetti. 2011. “Slices of the Unitary Spread.” Journal of Algebraic Combinatorics 33 (1): 37–56.
Chicago author-date (all authors)
Lunardon, Guglielmo, Laura Parlato, Valentina Pepe, and Rocco Trombetti. 2011. “Slices of the Unitary Spread.” Journal of Algebraic Combinatorics 33 (1): 37–56.
Vancouver
1.
Lunardon G, Parlato L, Pepe V, Trombetti R. Slices of the unitary spread. JOURNAL OF ALGEBRAIC COMBINATORICS. 2011;33(1):37–56.
IEEE
[1]
G. Lunardon, L. Parlato, V. Pepe, and R. Trombetti, “Slices of the unitary spread,” JOURNAL OF ALGEBRAIC COMBINATORICS, vol. 33, no. 1, pp. 37–56, 2011.
@article{1250795,
  abstract     = {We prove that slices of the unitary spread of Q(+)(7, q), q equivalent to 2 (mod 3), can be partitioned into five disjoint classes. Slices belonging to different classes are non-equivalent under the action of the subgroup of P Gamma O+(8, q) fixing the unitary spread. When q is even, there is a connection between spreads of Q(+)(7, q) and symplectic 2-spreads of PG(5, q) (see Dillon, Ph.D. thesis, 1974 and Dye, Ann. Mat. Pura Appl. (4) 114, 173-194, 1977). As a consequence of the above result we determine all the possible non-equivalent symplectic 2-spreads arising from the unitary spread of Q(+)(7, q), q = 2(2h+1). Some of these already appeared in Kantor, SIAM J. Algebr. Discrete Methods 3(2), 151-165, 1982. When q = 3(h), we classify, up to the action of the stabilizer in P Gamma O(7, q) of the unitary spread of Q(6, q), those among its slices producing spreads of the elliptic quadric Q(-)(5, q).},
  author       = {Lunardon, Guglielmo and Parlato, Laura and Pepe, Valentina and Trombetti, Rocco},
  issn         = {0925-9899},
  journal      = {JOURNAL OF ALGEBRAIC COMBINATORICS},
  keywords     = {OVOIDS,TRANSLATION-PLANES,Ovoid,Unitary spread,Slice},
  language     = {eng},
  number       = {1},
  pages        = {37--56},
  title        = {Slices of the unitary spread},
  url          = {http://dx.doi.org/10.1007/s10801-010-0232-x},
  volume       = {33},
  year         = {2011},
}

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