A theorem of completeness for families of compact analytic spaces
HTML articles powered by AMS MathViewer
- by John J. Wavrik
- Trans. Amer. Math. Soc. 163 (1972), 147-155
- DOI: https://doi.org/10.1090/S0002-9947-1972-0294702-5
- PDF | Request permission
Abstract:
A sufficient condition is given for a family of compact analytic spaces to be complete. This condition generalizes to analytic spaces the Theorem of Completeness of Kodaira and Spencer [6]. It contains, as a special case, the rigidity theorem proved by Schuster in [11].References
- M. Artin, On the solutions of analytic equations, Invent. Math. 5 (1968), 277–291. MR 232018, DOI 10.1007/BF01389777
- Adrien Douady, Le problème des modules pour les sous-espaces analytiques compacts d’un espace analytique donné, Ann. Inst. Fourier (Grenoble) 16 (1966), no. fasc. 1, 1–95 (French). MR 203082 —, Le problème des modules pour les variétés analytiques complexes, Séminaire Bourbaki 1964/65, exposé 277, Benjamin, New York, 1966. MR 33 #54201. A. Grothendieck, Techniques de construction en géométrie analytique I-X, Séminaire Henri Cartan 1960/61, 2ième éd., École Normale Supérieure, Secréetariat mathématique, Paris 1962. MR 26 #3562.
- K. Kodaira and D. C. Spencer, On deformations of complex analytic structures. I, II, Ann. of Math. (2) 67 (1958), 328–466. MR 112154, DOI 10.2307/1970009
- K. Kodaira and D. C. Spencer, A theorem of completeness for complex analytic fibre spaces, Acta Math. 100 (1958), 281–294. MR 112155, DOI 10.1007/BF02559541
- M. Kuranishi, On the locally complete families of complex analytic structures, Ann. of Math. (2) 75 (1962), 536–577. MR 141139, DOI 10.2307/1970211
- M. Kuranishi, New proof for the existence of locally complete families of complex structures, Proc. Conf. Complex Analysis (Minneapolis, 1964) Springer, Berlin, 1965, pp. 142–154. MR 0176496
- Geneviève Pourcin, Théorème de Douady au-dessus de $S$, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 23 (1969), 451–459 (French). MR 257402
- Michael Schlessinger, Functors of Artin rings, Trans. Amer. Math. Soc. 130 (1968), 208–222. MR 217093, DOI 10.1090/S0002-9947-1968-0217093-3
- Hans Werner Schuster, Über die Starrheit kompakter komplexer Räume, Manuscripta Math. 1 (1969), 125–137 (German, with English summary). MR 254269, DOI 10.1007/BF01173098
- Hans Werner Schuster, Zur Theorie der Deformationen kompakter komplexer Räume, Invent. Math. 9 (1969/70), 284–294. MR 268921, DOI 10.1007/BF01425483
- John J. Wavrik, Deformations of Banach [branched] coverings of complex manifolds, Amer. J. Math. 90 (1968), 926–960. MR 233384, DOI 10.2307/2373491
- John J. Wavrik, Obstructions to the existence of a space of moduli, Global Analysis (Papers in Honor of K. Kodaira), Univ. Tokyo Press, Tokyo, 1969, pp. 403–414. MR 0254882
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 163 (1972), 147-155
- MSC: Primary 32G05
- DOI: https://doi.org/10.1090/S0002-9947-1972-0294702-5
- MathSciNet review: 0294702