PROJECTIVE PLANE CURVES WHOSE AUTOMORPHISM GROUPS ARE SIMPLE AND PRIMITIVE

被引：1

作者：

Yoshida, Yusuke ^{[1
]}

机构：

[1] Hiroshima Univ, Grad Sch Adv Sci & Engn, Math Program, 1-3-1 Kagamiyama, Higashihiroshima, Hiroshima 7398526, Japan

来源：

KODAI MATHEMATICAL JOURNAL | 2021年 / 44卷 / 02期

关键词：

plane curves; invariant curves; automorphism groups; the icosahedral group; the Valentiner group; the Hessian group;

D O I：

10.2996/kmj44208

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study complex projective plane curves with a given group of automorphisms. Let G be a simple primitive subgroup of PGL(3, C), which is isomorphic to A(6), A(5) or PSL(2, F-7). We obtain a necessary and sufficient condition on d for the existence of a nonsingular projective plane curve of degree d invariant under G. We also study an analogous problem on integral curves.

引用

页码：334 / 368

页数：35

共 9 条

[1] Automorphism Groups of Nonsingular Plane Curves of Degree 5 [J].

Badr, Eslam ;

Bars, Francesc .

COMMUNICATIONS IN ALGEBRA, 2016, 44 (10) :4327-4340

[2]

Elkies N., 1999, Math. Sci. Res. Inst. Publ., V35, P51

[3]

Grass S, 1999, EXP MATH, V8, P209

[4]

Harui T., ARXIV170905V1 ARXIV170905V1, pII

[5] AUTOMORPHISM GROUPS OF SMOOTH PLANE CURVES [J].

Harui, Takeshi .

KODAI MATHEMATICAL JOURNAL, 2019, 42 (02) :308-331

[6]

Hurwitz A., 1892, Math. Ann., V41, P403

[7]

Klein Felix, 1878, Math. Ann., V14, P428, DOI [DOI 10.1007/BF01677143, 10.1007/BF01677143]

[8] FINITE UNITARY REFLECTION GROUPS [J].

SHEPHARD, GC ;

TODD, JA .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1954, 6 (02) :274-304

[9]

Wiman A., 1896, Mathematische Annalen, V47, P531

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