Castelnuovo不等式上界的一个注记

赵正俊

数学学报 ›› 2015, Vol. 58 ›› Issue (3) : 373-378.

PDF(411 KB)
中国科学院数学与系统科学研究院期刊网
PDF(411 KB)
数学学报 ›› 2015, Vol. 58 ›› Issue (3) : 373-378. DOI: 10.12386/A2015sxxb0038
论文

Castelnuovo不等式上界的一个注记

    赵正俊
作者信息 +

A Note on the Bound of Castelnuovo's Inequality

    Zheng Jun ZHAO
Author information +
文章历史 +

摘要

研究了Kummer函数域与Artin—Schreier函数域的复合域中素除子的分歧状况,由此给出了某些特殊情形下该复合域的亏格公式.从而给出复合函数域亏格公式达到Castelnuovo不等式的上界的一个例子,进而说明Castelnuovo上界确实是最优上界.

Abstract

We present some explicit formulae for genus of the composite field of Kummer and Artin-Schreier function fields in some specific cases. Meanwhile, we point out in this note that the genus of function field we addressed reaches the upper bound of Castelnuovo's inequality.

关键词

Kummer函数域 / Artin&mdash / Schreier函数域 / 差积除子 / 亏格

Key words

Kummer function fields / Artin-Schreier function fields / different divisor / genus

引用本文

EndNote

Ris (Procite)

Bibtex

导出引用
赵正俊. Castelnuovo不等式上界的一个注记. 数学学报, 2015, 58(3): 373-378 https://doi.org/10.12386/A2015sxxb0038
Zheng Jun ZHAO. A Note on the Bound of Castelnuovo's Inequality. Acta Mathematica Sinica, Chinese Series, 2015, 58(3): 373-378 https://doi.org/10.12386/A2015sxxb0038

参考文献

[1] Garcia A., Stichtenoth H., Elementary abelian p-extensions of algebraic function fields, Manus. Math., 1991, 72(1): 67-79.

[2] Hasse H., Theorie der relativ-zyklischen algebraischen Funktionenkörper insbesondere bei endlichem Konstantenkörper, J. Reine. Angew. Math., 1934, 172: 37-54.

[3] Hu S., Li Y., The genus fields of Artin-Schreier extensions, Finite Fields Appl., 2010, 16(4): 255-264.

[4] Stichtenoth H., Algebraic Function Fields and Codes, Springer-Verlag, Berlin, 2009.

[5] Stichtenoth H., Die Ungleichung von Castelnuovo, J. Reine. Angew. Math., 1983, 348: 197-202.

[6] Xing C. P., Multiple Kummer extension and the number of prime divisors of degree one in function fields, J. Pure Appl. Alge., 1993, 84(1): 85-93.

基金

国家自然科学基金资助项目(11326052, 31400714, 11301071, 11471154)

PDF(411 KB)

366

Accesses

0

Citation

Detail
段落导航
相关文章

/

〈 〉