Maximum number of points on intersection of a cubic surface and a non-degenerate Hermitian surface
| Autor: | Peter Beelen, Mrinmoy Datta |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Surface (mathematics)
Cubic surface Conjecture Intersection of surfaces Degree (graph theory) General Mathematics 010102 general mathematics Degenerate energy levels 01 natural sciences Hermitian matrix 14G05 14G15 05B25 Hermitian surfaces Combinatorics 03 medical and health sciences Mathematics - Algebraic Geometry 0302 clinical medicine Cubic surfaces Intersection FOS: Mathematics Rational points 030212 general & internal medicine 0101 mathematics Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Beelen, P & Datta, M 2020, ' Maximum number of points on intersection of a cubic surface and a non-degenerate Hermitian surface ', Moscow Mathematical Journal, vol. 20, no. 3, pp. 453-474 . https://doi.org/10.17323/1609-4514-2020-20-3-453-474 |
| DOI: | 10.17323/1609-4514-2020-20-3-453-474 |
| Popis: | In 1991 Sørensen proposed a conjecture for the maximum number of points on the intersection of a surface of degree d and a non-degenerate Hermitian surface in P3(Fq2). The conjecture was proven to be true by Edoukou in the case when d = 2. In this paper, we prove that the conjecture is true for d = 3. For q ≥ 4, we also determine the second highest number of rational points on the intersection of a cubic surface and a non-degenerate Hermitian surface. Finally, we classify all the cubic surfaces that admit the highest and, for q ≥ 4, the second highest number of points in common with a non-degenerate Hermitian surface. This classification disproves a conjecture proposed by Edoukou, Ling and Xing. |
| Databáze: | OpenAIRE |
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