Fields of moduli and fields of definition of odd signature curves

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• 作者：Michela Artebani (1)
  Saül Quispe (1)
  
• 关键词：14H37 ; 14H10 ; 14H45 ; Algebraic curves ; Field of moduli ; Field of definition
• 刊名：Archiv der Mathematik
• 出版年：2012
• 出版时间：October 2012
• 年：2012
• 卷：99
• 期：4
• 页码：333-344
• 全文大小：245KB
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• 作者单位：Michela Artebani (1)
  Saül Quispe (1)
  
  1. Departamento de Matemática, Universidad de Concepción, Concepción, Casilla 160-C, Chile
  
• ISSN：1420-8938

文摘

Let X be a smooth projective curve of genus ${g \geq 2}$ defined over a field K. We show that X can be defined over its field of moduli K X if the signature of the covering ${X \rightarrow X/ Aut(X)}$ is of type ${(0;c_1,\dots,c_k)}$ , where some c i appears an odd number of times. This result is applied to cyclic q-gonal curves and to plane quartics.