Hostname: page-component-6bb9c88b65-spzww Total loading time: 0 Render date: 2025-07-25T21:17:06.167Z Has data issue: false hasContentIssue false
  • English
  • Français

On moduli of stable quasi abelian varieties

Published online by Cambridge University Press:  22 January 2016

Iku Nakamura
Iku Nakamura*
Affiliation:
Mathematical Institute Faculty of Science Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In [4] Deligne-Mumford introduced a concept of stable curves and proved the existence of the coarse moduli space of stable curves of given genus in the category of algebraic stacks. Thereafter Mumford has shown this coarse moduli space is a protective scheme. We can consider the coarse moduli space of stable curves as a geometric compactification of the coarse moduli space of non-singular curves.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 58 , September 1975 , pp. 149 - 214
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

[1] Artin, M.: Algebraization of formal moduli I, Global Analysis (Papers in honor of Kodaira) Univ. Tokyo Press, Princeton Univ. Press (1969), 21–71.Google Scholar
[2] Artin, M.: Algebraic approximation of structures over complete local rings volume Dédié au Professeur Oscas Zariski; Publ. math. I.H.E.S. No. 36, Paris, 1969, 23–58. l’université de Montréal (1973).Google Scholar
[3] Artin, M.: théorèmes de représentabilité pour les espaces algébriques, les presses de Google Scholar
[4] Deligne, P. and Mumford, D.: The irreducibility of the space of curves of given genus, Volume Dédié au Professeur Oscar Zariski, Publ. math. I.H.E.S., Paris, 1969, 75–110.Google Scholar
[5] Deligne, P. and Rapoport, M.: Let schémas des modules de courbes elliptiques. Springer Berlin 349 (1972), 143–316.Google Scholar
[6] Grothendieck, A. and Dieudonné, J.: Elements de géométrie algebrique, Publ. Math. I.H.E.S., Paris 1960 ff.Google Scholar
[7] Hartshorne, R.: Local cohomology, Springer Berlin.Google Scholar
[8] Igusa, J.: A desingularization problem in the theory of Siegel modular functions, Math. Annalen 168 (1967), 228–260.Google Scholar
[9] Igusa, J.: Theta functions, Springer Berlin, Band 194 (1972).CrossRefGoogle Scholar
[10] Igusa, J.: Fiber systems of Jacobian varieties, Amer. J. Math. 81 (1959), 453–476.Google Scholar
[11] Knudsen, F., Mumford, D. et al.: Troidal embeddings I, II, Springer Berlin.Google Scholar
[12] Mumford, D.: Geometric invariant theory, Springer Berlin Band 34 (1970).Google Scholar
[13] Mumford, D.: An analytic construction of degenerating abelian varieties over complete rings, Composito Math. Vol. 24, Fasc. 3 (1972), 239–272.Google Scholar
[14] Mumford, D.: A new approach to compactifying locally symmetric varieties (to appear).Google Scholar
[15] Nakamura, I.: On properfication of analytic Neron model and its application (in preparation).Google Scholar
[16] Namikawa, Y.: On the canonical holomorphic map from the moduli space of stable curves to the Igusa monoidal transform, Nagoya Math. J., Vol. 52 (1973), 197–259.Google Scholar
[17] Namikawa, Y.: Studies on degeneration, Springer Berlin 412 (1974), 165–210.Google Scholar
[18] Namikawa, Y.: A new compactification of the Siegel space and degeneration of abelian varieties (to appear).Google Scholar
[19] Neron, A.: Model minimaux des varieties abeliennes sur les corps locaux et globaux, Publ. math. I.H.E.S. 21.Google Scholar
[20] Oda, T. and Seshadri, C. S.: Compactification of the generalized Jacobian variety (to appear).Google Scholar
[21] Oda, T. and Miyake, K.: Almost homogeneous algebraic varieties under algebraic torus action, Manifolds 1973, Proceedings of the International Conference on manifolds and related topics in topology, Univ. Tokyo Press, 1974.Google Scholar
[22] Satake, I.: On the compactification of the Siegel space, J. Indian Math. Soc, Vol. 20 (1956), 259–281.Google Scholar
[23] Schlessinger, M.: Functor of Artin rings, Trans. Amer. Math. Soc, Vol. 130 (1968), 208–222.Google Scholar
[24] Schuster, H. W.: Deformationen analytischer Algebren, Invent, math. 6 (1968), 262–274.Google Scholar
[25] Ueno, K.: On fiber spaces of normally polarized abelian varieties of dimension 2, I-II, J. Fac. Soc. Univ. Tokyo, Vols. 18 and 19 (1971–1972), 33–95 and 163–199.Google Scholar
[26] Voronoi, G.: Nouvelles applicationss des parametres continus a la theorie des formes quadratiques, I, II, III, J. Reine Angew. Math., Bd. 133 (1908), 97–108; Bd. 134 (1908), 198–287; Bd. 136 (1909), 67–181.Google Scholar
[27] Wavrik, J.: A theorem of completeness for families of compact analytic spaces, Trans. Amer. Math. Soc. 163 (1972), 147–155.Google Scholar
[28] Satake, I.: On the arithmetic of tube domains, Bulletin A.M.S., 79 (1973), 1076-1094.Google Scholar
[29] Ueno, K.: Degenerated fibers of families of abelian varieties of dimension 2 (unpublished).Google Scholar