Fields of moduli and definition of hyperelliptic covers

被引：9

作者：

Fuertes, Y. ^{[1
]}

Gonzalez-Diez, G. ^{[1
]}

机构：

[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

来源：

ARCHIV DER MATHEMATIK | 2006年 / 86卷 / 05期

关键词：

D O I：

10.1007/s00013-005-1433-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, for all genera g > 1, g equivalent to 1 mod 4, we construct an explicit hyperelliptic curve whose field of moduli is Q and such that the minimum subfield of R over which it can be hyperelliptically defined is a degree three extension of Q. These examples are related to previous work by Earle, Shimura, and Mestre and to a recent conjecture by Shaska.

引用

页码：398 / 408

页数：11

共 16 条

[1] ON THEORY OF THETA-FUNCTIONS, MODULI OF ABELIAN VARIETIES, AND MODULI OF CURVES [J].

BAILY, WL .

ANNALS OF MATHEMATICS, 1962, 75 (09) :342-&

[2]

EARLE CJ, 1971, ANN MATH STUD, V66

[3]

Farkas H. M., 1980, RIEMANN SURFACES, DOI [10.1007/978-1-4612-2034-3, DOI 10.1007/978-1-4612-2034-3]

[4]

FUERTES Y, UNPUB SMOOTH NORMAL

[5]

FUERTES Y, 1993, PUBL MAT, V37, P339

[6]

GONZALEZDIEZ G, 1992, LOND MATH S, V173, P75, DOI 10.1017/CBO9780511565793.010

[7]

GONZALEZDIEZ G, 1991, P LOND MATH SOC, V62, P469, DOI [DOI 10.1112/PLMS/S3-62.3.469, 10.1112/plms/s3-62.3]

[8]

GONZALEZDIEZ G, UNPUB VARIATIONS BEL

[9]

HORIUCHI R, 1979, J MATH KYOTO U, V19

[10]

Hungerford T.W., 1974, Algebra

← 1 2 →