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The coincidence of fields of moduli for non-hyperelliptic curves and for their jacobian varieties

Published online by Cambridge University Press:  22 January 2016

Tsutomu Sekiguchi
Affiliation:
Department of Mathematics, Faculty of Science and Engineering, Chuo University, Kasuga, Bunkyo-ku Tokyo, Japan
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Extract

The notion of fields of moduli introduced first by Matsusaka [8] has been developed by Shimura [12] exclusively in the area of polarized abelian varieties. Later Koizumi [7] gave an axiomatic treatment for the notion.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

References

[1] Bourbaki, N., Algèbre, Eléments de Math. 23, Hermann, Paris, 1958.Google Scholar
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[3] Deligne, P. and Mumford, D., The irreducibility of the space of curves of given genus, Publ. Math., 36 (Volume dedicated to Zariski, O.), I.H.E.S. (1969), 75109.CrossRefGoogle Scholar
[4] Grothendieck, A., Fondements de la géométrie algébrique, Séminaire Bourbaki 1957–62, Secrétariat Math., Paris (1962).Google Scholar
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[6] Grothendieck, A. et al., Séminaire de géométrie algébrique 1, Lecture notes in 224, Springer-Verlag, Heidelberg, 1971. Refered to as SGA 1.Google Scholar
[7] Koizumi, S., The fields of moduli for polarized abelian varieties and for curves, Nagoya Math. J., 48 (1972), 3755.CrossRefGoogle Scholar
[8] Matsusaka, T., Polarized varieties, fields of moduli and generalized Kummer varieties of polarized abelian varieties, Amer. J. Math., 80 (1958), 4582.CrossRefGoogle Scholar
[9] Mumford, D., Geometric invariant theory, Ergebnisse, Springer-Verlag, Heidelberg, 1965.CrossRefGoogle Scholar
[10] Oort, F., Finite group schemes, local moduli for abelian varieties and lifting problems, algebraic geometry, Oslo 1970, Proceedings of the 5th Nordic Summer-School in Math., edited by Oort, F..Google Scholar
[11] Oort, F. and Ueno, K., Principally polarized abelian varieties of dimension two or three are Jacobian varieties, J. Fac. Sci. Univ. Tokyo, Section IA, Math., 20 (1973), 377381.Google Scholar
[12] Shimura, G., On the theory of automorphic functions, Ann. of Math., 76 (1959), 101144.CrossRefGoogle Scholar
[13] Shimura, G., On the field of rationality for an abelian variety, Nagoya Math. J., 45 (1972), 167178.Google Scholar

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