Characterization of non-singular hyperplanes of H(s,q²) in P G(s, q²)

2025/06/29 by Stuti Mohanty, Mohanty, Stuti, Bikramaditya Sahu +1
Mathematics · #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2506.23330

openalex publication_date 2025/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we present a combinatorial characterization of the hyperplanes associated with non-singular hermitian varieties H(s, q²) in the projective space PG(s,q²) where s≥3 and q>2. By analyzing the intersection numbers of hyperplanes with points and co-dimension 2 subspaces, we establish necessary and sufficient conditions for a hyperplane to be part of the hermitian variety. This approach extends previous characterizations of hermitian varieties based on intersection properties, providing a purely combinatorial method for identifying their hyperplanes.

Citations

• Characterizing parabolic hyperplanes of the hyperbolic and elliptic quadrics in PG(2n + 1, q)
• Characterising elliptic and hyperbolic hyperplanes of the parabolic\n quadric Q(2n,q)
• Characterising elliptic solids of Q(4,q), q even
• Characterising hyperbolic hyperplanes of a non-singular quadric in PG(4,q)

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• Maximum number of points of intersection of a non-degenerate Hermitian variety and a cubic hypersurface