Geodesic
Partitioning Projective Geometries into Caps
Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1163-1175

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In [2] by means of a fairly lengthy argument involving Hermitian varieties it was shown that PG(2n, q 2) can be partitioned into (q 2n++ 1 + 1)/(q + l)-caps. Moreover, these caps were shown to constitute the “large points” of a PG(2n, q) in a natural way. In [3] a similar argument was used to show that once two disjoint (n – l)-subspaces are removed from PG(2n, q 2), the remaining points can be partitioned into (q 2n – 1)/(q 2 – l)-caps.The purpose of this paper is to give a short proof of the results found in [2], and then use the technique developed to partition PG(2n, q) into (qn + l)-caps for n even and q any prime-power. Moreover, these caps can be treated in a natural way as the “large points” of a PG(n – 1, q). 
Ebert, Gary L. Partitioning Projective Geometries into Caps. Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1163-1175. doi: 10.4153/CJM-1985-063-1
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[1] 1. Barlotti, A., Un'estensione del teorema di Segre-Kustaanheimo, Boll. Un. Mat. Ital. 10 (1955), 498–506. Google Scholar

[2] 2. Kestenband, B. C., Projective geometries that are disjoint unions of caps, Can. J. Math. 32 (1980), 1299–1305. Google Scholar

[3] 3. Kestenband, B. C., Hermitian configurations in odd-dimensional projective geometries, Can. J. Math. 33 (1981), 500–512. Google Scholar

[4] 4. Qvist, B., Some remarks concerning curves of the second degree in a finite plane, Ann. Acad. Sci. Fenn. 734 (1952), 1–27. Google Scholar

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