Topic
Hermitian variety
About: Hermitian variety is a research topic. Over the lifetime, 73 publications have been published within this topic receiving 1135 citations.
Papers published on a yearly basis
Papers
TL;DR: In this article, it was shown that the number of rational points of a projective, geometrically irreducible, non-singular, algebraic curve defined over a finite field Fq2 of order q 2 satisfies the Hasse-Weil upper bound.
Abstract: Let X be a projective, geometrically irreducible, non-singular, algebraic curve defined over a finite field Fq2 of order q2 If the number of Fq2-rational points of X satisfies the Hasse–Weil upper bound, then X is said to be Fq2-maximal For a point P0 ∈ X(Fq2), let π be the morphism arising from the linear series D: = |(q + 1)P0|, and let N: = dim(D) It is known that N ≥ 2 and that π is independent of P0 whenever X is Fq2-maximal
40 citations
TL;DR: It is proved that if Sis any symplectic spread PG(3, q), then the extended lines of this spread form a complete (q2 + 1)-span of H, and extensions to higher dimensions are discussed, showing in particular that a similar construction produces complete ( q3 + 1-spans of the Hermitian variety H(5, q2).
Abstract: Let \mathcal{L} be a general linear complex in PG(3, q) for any prime power q. We show that when GF(q) is extended to GF(q2), the extended lines of \mathcal{L} cover a non-singular Hermitian surface H ≅ H(3, q2) of PG(3, q2). We prove that if \mathcal{S} is any symplectic spread PG(3, q), then the extended lines of this spread form a complete (q2 + 1)-span of H. Several other examples of complete spans of H for small values of q are also discussed. Finally, we discuss extensions to higher dimensions, showing in particular that a similar construction produces complete (q3 + 1)-spans of the Hermitian variety H(5, q2).
33 citations
TL;DR: In this paper, the section of a non-degenerate Hermitian variety V N −1 by a polar hyperplane in PG( N, q 2 ) and the number of u -flats, 0 ≤ u ≤ [ (N − 1) 2 ], contained in a V n −1 are derived.
26 citations
TL;DR: It is shown in this paper that this set of lines of Q(4,q), q even, does not contain minimal covers of sizes q2+1+r when q⩾32 and 0
22 citations
TL;DR: In this article, the authors present several old and new results concerning substructures (e.g., partial spreads, ovoids, and tight sets) of polar spaces, and present several new results for polar spaces.
Abstract: We present several old and new results concerning substructures (e.g. partial spreads, ovoids, and tight sets) of polar spaces.
22 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2020 | 4 |
| 2019 | 2 |
| 2018 | 2 |
| 2017 | 2 |
| 2016 | 4 |