The sizes of the intersection of two unitals in PG(2,q²)

2011/07/09 by David B. Chandler, Chandler, David B.
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1107.1820

arxiv created 2011/07/09 · openalex publication_date 2011/07/09 · arxiv updated 2011/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the size of the intersection of a Hermitian variety in \PG(n,q²), and any set satisfying an r-dimensional-subspace intersection property, is congruent to 1 modulo a power of p. In particular, in the case where n=2, if the two sets are a Hermitian unital and any other unital, the size of the intersection is congruent to 1 modulo √ q or modulo √(pq). If the second unital is a Buekenhout-Metz unital, we show that the size is congruent to 1 modulo q.

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