- Author
- Guglielmo Lunardon, Laura Parlato, Valentina Pepe (UGent) and Rocco Trombetti
- Organization
- 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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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-1250795
- MLA
- Lunardon, Guglielmo, et al. “Slices of the Unitary Spread.” JOURNAL OF ALGEBRAIC COMBINATORICS, vol. 33, no. 1, 2011, pp. 37–56, doi:10.1007/s10801-010-0232-x.
- APA
- Lunardon, G., Parlato, L., Pepe, V., & Trombetti, R. (2011). Slices of the unitary spread. JOURNAL OF ALGEBRAIC COMBINATORICS, 33(1), 37–56. https://doi.org/10.1007/s10801-010-0232-x
- 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. https://doi.org/10.1007/s10801-010-0232-x.
- 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. doi:10.1007/s10801-010-0232-x.
- 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://doi.org/10.1007/s10801-010-0232-x}},
volume = {{33}},
year = {{2011}},
}
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