 Author
 Anamari Nakić and Leo Storme (UGent)
 Organization
 Abstract
 We show that every itight set in the Hermitian variety H(2r + 1, q) is a union of pairwise disjoint (2r + 1)dimensional Baer subgeometries PG(2r + 1, root q) and generators of H(2r + 1, q), if q >= 81 is an odd square and i < (q(2/3)  1)/2. We also show that an itight set in the symplectic polar space W(2r + 1, q) is a union of pairwise disjoint generators of W(2r + 1, q), pairs of disjoint rspaces {Delta,Delta(perpendicular to)}, and (2r + 1)dimensional Baer subgeometries. For W(2r + 1, q) with r even, pairs of disjoint rspaces {Delta,Delta(perpendicular to)} cannot occur. The (2r + 1)dimensional Baer subgeometries in the itight set of W(2r + 1, q) are invariant under the symplectic polarity perpendicular to of W(2r + 1, q) or they arise in pairs of disjoint Baer subgeometries corresponding to each other under perpendicular to. This improves previous results where i < q(5/8)/root 2+ 1 was assumed. Generalizing known techniques and using recent results on blocking sets and minihypers, we present an alternative proof of this result and consequently improve the upper bound on i to (q(2/3)  1)/2. We also apply our results on tight sets to improve a known result on maximal partial spreads in W(2r + 1, q).
 Keywords
 Tight sets, finite classical polar spaces, minihypers, blocking sets, Hermitian varieties, symplectic polar spaces, MULTIPLE BLOCKING SETS, BAER SUBPLANES, MINIHYPERS, ARCS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU8517621
 Chicago
 Nakić, Anamari, and Leo Storme. 2017. “Tight Sets in Finite Classical Polar Spaces.” Advances in Geometry 17 (1): 109–129.
 APA
 Nakić, A., & Storme, L. (2017). Tight sets in finite classical polar spaces. ADVANCES IN GEOMETRY, 17(1), 109–129.
 Vancouver
 1.Nakić A, Storme L. Tight sets in finite classical polar spaces. ADVANCES IN GEOMETRY. 2017;17(1):109–29.
 MLA
 Nakić, Anamari, and Leo Storme. “Tight Sets in Finite Classical Polar Spaces.” ADVANCES IN GEOMETRY 17.1 (2017): 109–129. Print.
@article{8517621, abstract = {We show that every itight set in the Hermitian variety H(2r + 1, q) is a union of pairwise disjoint (2r + 1)dimensional Baer subgeometries PG(2r + 1, root q) and generators of H(2r + 1, q), if q >= 81 is an odd square and i < (q(2/3)  1)/2. We also show that an itight set in the symplectic polar space W(2r + 1, q) is a union of pairwise disjoint generators of W(2r + 1, q), pairs of disjoint rspaces {Delta,Delta(perpendicular to)}, and (2r + 1)dimensional Baer subgeometries. For W(2r + 1, q) with r even, pairs of disjoint rspaces {Delta,Delta(perpendicular to)} cannot occur. The (2r + 1)dimensional Baer subgeometries in the itight set of W(2r + 1, q) are invariant under the symplectic polarity perpendicular to of W(2r + 1, q) or they arise in pairs of disjoint Baer subgeometries corresponding to each other under perpendicular to. This improves previous results where i < q(5/8)/root 2+ 1 was assumed. Generalizing known techniques and using recent results on blocking sets and minihypers, we present an alternative proof of this result and consequently improve the upper bound on i to (q(2/3)  1)/2. We also apply our results on tight sets to improve a known result on maximal partial spreads in W(2r + 1, q).}, author = {Nakić, Anamari and Storme, Leo}, issn = {1615715X}, journal = {ADVANCES IN GEOMETRY}, keywords = {Tight sets,finite classical polar spaces,minihypers,blocking sets,Hermitian varieties,symplectic polar spaces,MULTIPLE BLOCKING SETS,BAER SUBPLANES,MINIHYPERS,ARCS}, language = {eng}, number = {1}, pages = {109129}, title = {Tight sets in finite classical polar spaces}, url = {http://dx.doi.org/10.1515/advgeom20160034}, volume = {17}, year = {2017}, }
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