Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-24T23:33:56.688Z Has data issue: false hasContentIssue false

On the douady space of a compact complex space in the category

Published online by Cambridge University Press:  22 January 2016

Akira Fujiki*
Affiliation:
Kyoto 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.

Let X be a complex space. Let Dx be the Douady space of compact complex subspaces of X [6] and px: Zx→ Dx the corresponding universal family of subspaces of X.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

[ 1 ] Artin, M., Algebraization of formal moduli, I, II, in Collected papers in Honor of Kodaira K., Univ. of Tokyo Press and Princeton Univ. Press, (1969), 21-72 and Ann. of Math., 91 (1970), 88135.Google Scholar
[ 2 ] Banica, C, Un théorème concernant les familles analytiques d’espaces complexes, Rev. Roumaine Math. Pures Appl., 18 (1973), 15151520.Google Scholar
[ 3 ] Banica, C. and Stanasila, O., Algebraic methods in the global theory of complex spaces, John Wiley & Sons and Editura Academiei 1976.Google Scholar
[ 4 ] Barlet, D., Espace analytique reduit des cycles analytiques complexes de dimension finie, Seminaire Norguet F., Lecture Notes in Math., No. 482, 1158. Springer 1975.Google Scholar
[ 5 ] Campana, F., Algébricité et compacité dans l’espace des cycles d’un espace analytique complexe, Math. Ann., 251 (1980), 718.Google Scholar
[ 6 ] Douady, A., Le probléme de modules pour les sous-espaces analytique donné, Ann. Inst. Fourier, Grenoble, 16 (1966), 195.Google Scholar
[ 7 ] Fischer, G., Complex analytic geometry, Lecture Notes in Math., No. 538 Springer 1976.Google Scholar
[ 8 ] Frisch, J., Points de platitude d’un morphism d’espaces analytiques complexes, Inventiones math., 4 (1967), 118138.Google Scholar
[ 9 ] Fujiki, A., Closedness of the Douady spaces of compact Kähler spaces, Publ. RIMS, Kyoto Univ., 14 (1978), 152.Google Scholar
[10] Fujiki, A., On automorphism groups of compact Káhler manifolds, Inventiones math., 44 (1978), 225258.Google Scholar
[11] Fujiki, A., Deformations of uniruled manifolds, Publ. RIMS, Kyoto Univ., 17 (1981), 687702.Google Scholar
[12] Grothendieck, A., Fondements de la géométrie algébrique (Extraits du Seminaire Bourbaki 1957-1962), Paris 1962.Google Scholar
[13] Grothendieck, A, Technique de construction en géométrie analytique, Séminaire Henri Cartan, 13e annee (1960/61).Google Scholar
[14] Hironaka, H., Flattening theorem in complex-analytic geometry, Amer. J. Math., 97 (1975), 503547.Google Scholar
[15] Hironaka, H., Bimeromorphic smoothing of a complex-analytic space, Math. Inst. Warwick Univ., England 1971.Google Scholar
[16] Hironaka, H., Leujeune-Jalabert, M. and Teissier, B., Platificateur local en géométrie analytique et applatissement local, Astérisque, 78 (1973), 441463.Google Scholar
[17] Moishezon, B., Modifications of complex varieties and the Chow lemma, Lecture Notes in Math., No. 412, Springer 1974, 133139.Google Scholar
[18] Pourcin, G., Théorème de Douady audessus de S, Ann. Sci. Norm. Sup. di Pisa, 23 (1969), 451459.Google Scholar
[19] Raynaud, M. and Gruson, L., Critère de platitude de projectivité, Inventiones math., 13 (1971), 189.Google Scholar
[20] Rossi, H., Picard varieties of an isolated singular point, Rice Univ. Studies, 54 (1968), 6373.Google Scholar
[21] Ueno, K., Classification theory of algebraic varieties and compact complex spaces, Lecture Notes in Math., No. 438, Springer 1975.Google Scholar