Classification of cubic surfaces with twenty-seven lines over the finite field of order thirteen

被引：5

作者：

Betten, Anton ^{[1
]}

Hirschfeld, James W. P. ^{[2
]}

Karaoglu, Fatma ^{[2
]}

机构：

[1] Colorado State Univ, Dept Math, Louis R Weber Bldg, Ft Collins, CO 80523 USA

[2] Univ Sussex, Dept Math, Pevensey Bldg, Brighton BN1 9QH, E Sussex, England

来源：

EUROPEAN JOURNAL OF MATHEMATICS | 2018年 / 4卷 / 01期

关键词：

Cubic surface; Double-six; Finite field;

D O I：

10.1007/s40879-017-0182-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In Hirschfeld (J Austral Math Soc 4(1):83-89, 1964), the existence of the cubic surface which arises from a double-six over the finite field of order four was considered. In Hirschfeld (Rend Mat Appl 26:115-152, 1967), the existence and the properties of the cubic surfaces over the finite fields of odd and even order was discussed and classified over the fields of order seven, eight, nine. In this paper, cubic surfaces with twenty-seven lines over the finite field of thirteen elements are classified.

引用

页码：37 / 50

页数：14

共 13 条

[1]

Baker H.F, 1960, PRINCIPLES GEOMETRY, VIII

[2]

Betten A, 2016, DESIGN CODE CRYPTOGR, V79, P583, DOI 10.1007/s10623-015-0074-6

[3]

Clebsch Alfred, 1866, J REINE ANGEW MATH, V65, P359

[4]

EDGE WL, 1959, CAN J MATH, V11, P625

[5]

Hirschfeld J., 1998, OXFORD MATH MONOGRAP

[6]

Hirschfeld J.W.P, 1985, FINITE PROJECTIVE SP

[7]

Hirschfeld JWP., 1967, REND MAT APPL, V26, P115

[8]

Hirschfeld JWP., 1964, J AUSTR MATH SOC, V4, P83, DOI DOI 10.1017/S144678870002276X

[9]

Sadeh A R, 1984, THESIS

[10]

Salmon G, 1849, CAMBRIDGE DUBLIN MAT, V4, P252

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