Hemisystems of the Hermitian surface

Autor(es)

Korchmaros, Gabor ^[1] ; Nagy, Gabor P. ^{[2, 3]} ; Speziali, Pietro ^{[4, 1]}

Afiliação do(s) autor(es)

^[1] Univ Basilicata, Dipartimento Matemat Informat & Econ, Viale Ateneo Lucano 10, I-85100 Potenza - Italy

^[2] Budapest Univ Technol & Econ, Dept Algebra, Egry Jozsef Utca 1, H-1111 Budapest - Hungary

^[3] Univ Szeged, Bolyai Inst, Szeged - Hungary

^[4] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF COMBINATORIAL THEORY SERIES A; v. 165, p. 408-439, JUL 2019.
• Citações Web of Science: 0

Resumo

We present a new method for the study of hemisystems of the Hermitian surface U-3 of PG(3, q(2)). The basic idea is to represent generator-sets of U-3 by means of a maximal curve naturally embedded in U-3 so that a sufficient condition for the existence of hemisystems may follow from results about maximal curves and their automorphism groups. In this paper we obtain a hemisystem in PG(3,p(2)) for each p prime of the form p = 1 + 16n(2) with an integer n. Since the famous Landau's conjecture dating back to 1904 is still to be proved (or disproved), it is unknown whether there exists an infinite sequence of such primes. What is known so far is that just 18 primes up to 51000 with this property exist, namely 17, 257, 401, 577, 1297, 1601, 3137, 7057, 13457, 14401, 15377, 24337, 25601, 30977, 32401, 33857, 41617, 50177. The scarcity of such primes seems to confirm that hemisystems of U-3 are rare objects. (C) 2018 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 17/18776-6 - Curvas algébricas em característica positiva e aplicações
• Beneficiário: Pietro Speziali
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado