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Line spreads of W(2n-1, q), q even
Abstract
Let q be an even prime power and n \ge 2. We construct line spreads of the symplectic polar space W(2n-1,q) by replacing pairwise disjoint reguli in a Desarguesian line spread. The construction is based on partitions of the points of PG(n-1,q^2) into points of a nondegenerate Hermitian variety and Baer sublines meeting that variety in exactly one point. In the plane case, the partition is invariant under a cyclic group of order q^2-q+ 1.
Related
BibTeX
@misc{bartoli2026line,
title = {{Line spreads of W(2n-1, q), q even}},
author = {Daniele Bartoli and Antonio Cossidente and Giuseppe Marino and Francesco Pavese},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23664},
eprint = {2610.23664},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23664},
}
RIS
TY - UNPB
TI - Line spreads of W(2n-1, q), q even
AU - Daniele Bartoli
AU - Antonio Cossidente
AU - Giuseppe Marino
AU - Francesco Pavese
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23664
UR - https://arxiv.org/abs/2610.23664
AB - Let q be an even prime power and n \ge 2. We construct line spreads of the symplectic polar space W(2n-1,q) by replacing pairwise disjoint reguli in a Desarguesian line spread. The construction is based on partitions of the points of PG(n-1,q^2) into points of a nondegenerate Hermitian variety and Baer sublines meeting that variety in exactly one point. In the plane case, the partition is invariant under a cyclic group of order q^2-q+ 1.
ER -