On maximal plane curves of degree 3 over F4, and Sziklai’s example of degree q − 1 over Fq.

Autor: Masaaki Homma

Publikováno v: Journal of Algebra Combinatorics Discrete Structures & Applications; 2024, Vol. 11 Issue 2, p127-138, 12p

A proof of Sørensen’s conjecture on Hermitian surfaces

Autor: Mrinmoy Datta, Masaaki Homma, Peter Beelen

Publikováno v: Beelen, P, Datta, M & Homma, M 2021, ' A proof of sørensen’s conjecture on hermitian surfaces ', Proceedings of the American Mathematical Society, vol. 149, no. 4, pp. 1431-1441 . https://doi.org/10.1090/proc/15331

In this article we prove a conjecture formulated by A. B. Sørensen in 1991 on the maximal number of F q 2 \mathbb {F}_{q^2} -rational points on the intersection of a non-degenerate Hermitian surface and a surface of degree d ≤ q . d \le q.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::430e66b8bc37c15ce5451a6ff05dbd9f
https://doi.org/10.1090/proc/15331

On Hermitian varieties in PG(6, q^2)

Autor: Luca Giuzzi, Angela Aguglia, Masaaki Homma

Publikováno v: Ars Mathematica Contemporanea. 21:#P1.04

In this paper we characterize the non-singular Hermitian variety ℋ(6, q 2 ) of PG(6, q 2 ) , q ≠ 2 among the irreducible hypersurfaces of degree q + 1 in PG(6, q 2 ) not containing solids by the number of its points and the existence of a solid S

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0376584f61fdd4d04427bc9b2c08092d
https://doi.org/10.26493/1855-3974.2358.3c9

On a number of rational points on a plane curve of low degree

Autor: Seon Jeong Kim, Eun Ju Cheon, Masaaki Homma, Namyong Lee

Publikováno v: Discrete Mathematics. 340:1327-1334

InHomma and Kim (2010), an upper bound of the number of rational points on a plane curve of degree d over Fq is found. Some examples attaining the bound are given inHomma and Kim (2010), whose degrees are q+2, q+1, q, q1, q1 (when q is a square), and

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https://doi.org/10.1016/j.disc.2017.01.017

Points on singular Frobenius nonclassical curves

Autor: Masaaki Homma, Herivelto Borges

Publikováno v: Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP

In 1990, Hefez and Voloch proved that the number of \(\mathbb {F}_q\)-rational points on a nonsingular plane q-Frobenius nonclassical curve of degree d is \(N=d(q-d+2)\). We address these curves in the singular setting. In particular, we prove that \

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b2555d4b582ae3dd9abe6d94f7a09d58
https://doi.org/10.1007/s00574-016-0008-6