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On the fields of rationality for curves and for their jacobian varieties

Published online by Cambridge University Press:  22 January 2016

Tsutomu Sekiguchi
Tsutomu Sekiguchi*
Affiliation:
Department of Mathematics, Faculty of Science and Engineering Chuo University, Kasuga, Bunkyo-ku Tokyo, Japan
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Throughout the paper, a scheme means a noetherian scheme. By a curve C over a scheme S of genus g, we mean a proper and smooth S-scheme with irreducible curves of genus g as geometric fibres. In the previous paper [15], the author showed that the field of moduli for a non-hyperelliptic curve over a field coincides with the one for its canonically polarized jacobian variety, and in [16], he gave a partial result on the coincidence of the fields of rationality for a hyperelliptic curve and for its canonically polarized jacobian variety. In the present paper, we will discuss the isomorphy of the isomorphism schemes of two curves over a scheme and of their canonically polarized jacobian schemes, by using Oort-Steenbrink’s result [12].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 88 , December 1982 , pp. 197 - 212
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

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