Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Analytic geometry of complex superspaces
HTML articles powered by AMS MathViewer

by H. Flenner and D. Sundararaman
Trans. Amer. Math. Soc. 330 (1992), 1-40
DOI: https://doi.org/10.1090/S0002-9947-1992-1069748-2

Abstract:

A detailed account of the analytic geometry of complex superspaces is given in this paper. Several representability criteria and representability theorems are proved. In particular, the existence of a versal family of deformations (parametrized by a complex superspace) for any compact complex superspace is proved.
References
  • M. Artin, On the solutions of analytic equations, Invent. Math. 5 (1968), 277–291. MR 232018, DOI 10.1007/BF01389777
  • M. Artin, Algebraization of formal moduli. I, Global Analysis (Papers in Honor of K. Kodaira), Univ. Tokyo Press, Tokyo, 1969, pp. 21–71. MR 0260746
  • M. Artin, Versal deformations and algebraic stacks, Invent. Math. 27 (1974), 165–189. MR 399094, DOI 10.1007/BF01390174
  • Felix Alexandrovich Berezin, Introduction to superanalysis, Mathematical Physics and Applied Mathematics, vol. 9, D. Reidel Publishing Co., Dordrecht, 1987. Edited and with a foreword by A. A. Kirillov; With an appendix by V. I. Ogievetsky; Translated from the Russian by J. Niederle and R. Kotecký; Translation edited by Dimitri Leĭtes. MR 914369, DOI 10.1007/978-94-017-1963-6
  • Jürgen Bingener, Über formale komplexe Räume, Manuscripta Math. 24 (1978), no. 3, 253–293 (German). MR 492367, DOI 10.1007/BF01167833
  • Jürgen Bingener, Darstellbarkeitskriterien für analytische Funktoren, Ann. Sci. École Norm. Sup. (4) 13 (1980), no. 3, 317–347 (German). MR 597743
  • Jürgen Bingener, Offenheit der Versalität in der analytischen Geometrie, Math. Z. 173 (1980), no. 3, 241–281 (German). MR 592373, DOI 10.1007/BF01159663
  • J. Bingener and S. Kosarew, Lokale Modulräume in der analytischen Geometrie, Vieweg, Braunschweig. P. Deligne, Letter to D. Sundararaman, April 7, 1987.
  • 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
  • H. Flenner, Deformationen holomorpher Abbildungen, Habilitationsschrift, Osnabrück, 1978.
  • Hubert Flenner, Eine Bemerkung über relative $\textrm {Ext}$-Garben, Math. Ann. 258 (1981/82), no. 2, 175–182 (German). MR 641823, DOI 10.1007/BF01450533
  • Hubert Flenner, Ein Kriterium für die Offenheit der Versalität, Math. Z. 178 (1981), no. 4, 449–473 (German). MR 638811, DOI 10.1007/BF01174768
  • J. Frisch, Aplatissement en géométrie analytique, Ann. Sci. École Norm. Sup. (4) 1 (1968), 305–312 (French). MR 236421
  • Hans Grauert, Der Satz von Kuranishi für kompakte komplexe Räume, Invent. Math. 25 (1974), 107–142 (German). MR 346194, DOI 10.1007/BF01390171
  • Hans Grauert, On meromorphic equivalence relations, Contributions to several complex variables, Aspects Math., E9, Friedr. Vieweg, Braunschweig, 1986, pp. 115–147. MR 859195
  • A. Grothendieck, Techniques de construction en géométrie analytique. ${\text {I}} - {\text {X}}$, Séminaire Cartan, 1960, 1962.
  • Robin Hartshorne, Residues and duality, Lecture Notes in Mathematics, No. 20, Springer-Verlag, Berlin-New York, 1966. Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64; With an appendix by P. Deligne. MR 0222093
  • Reinhardt Kiehl, Äquivalenzrelationen in analytischen Räumen, Math. Z. 105 (1968), 1–20 (German). MR 232964, DOI 10.1007/BF01135445
  • S. Kosarew and C. Okonek, Global moduli spaces and simple holomorphic bundles, Mathematica Gottingensis, Heft 10, 1987.
  • 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
  • D. A. Leĭtes, Introduction to the theory of supermanifolds, Uspekhi Mat. Nauk 35 (1980), no. 1(211), 3–57, 255 (Russian). MR 565567
  • Yu. I. Manin, New dimensions in geometry, Workshop Bonn 1984 (Bonn, 1984) Lecture Notes in Math., vol. 1111, Springer, Berlin, 1985, pp. 59–101. MR 797416, DOI 10.1007/BFb0084585
  • Yuri I. Manin, Gauge field theory and complex geometry, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 289, Springer-Verlag, Berlin, 1988. Translated from the Russian by N. Koblitz and J. R. King. MR 954833
  • V. P. Palamodov, Deformations of complex spaces, Uspehi Mat. Nauk 31 (1976), no. 3(189), 129–194 (Russian). MR 0508121
  • Geneviève Pourcin, Théorème de Douady au-dessus de $S$, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 23 (1969), 451–459 (French). MR 257402
  • R. S. Rim, Formal deformation theory, Groupes de Monodromie en Géométrie Algébrique (SGA7I), expose VI, Lecture Notes in Math., vol. 288, Springer-Verlag, Berlin and New York, 1972.
  • Jean-Pierre Ramis and Gabriel Ruget, Complexe dualisant et théorèmes de dualité en géométrie analytique complexe, Inst. Hautes Études Sci. Publ. Math. 38 (1970), 77–91 (French). MR 279338
  • Michael Schlessinger, Functors of Artin rings, Trans. Amer. Math. Soc. 130 (1968), 208–222. MR 217093, DOI 10.1090/S0002-9947-1968-0217093-3
  • H. W. Schuster, Formale Deformationstheorien, Habilitationsschrift, München, 1971.
  • Hans Werner Schuster, Infinitesimale Erweiterungen komplexer Räume, Comment. Math. Helv. 45 (1970), 265–286 (German). MR 276496, DOI 10.1007/BF02567331
  • Yum Tong Siu and Günther Trautmann, Deformations of coherent analytic sheaves with compact supports, Mem. Amer. Math. Soc. 29 (1981), no. 238, iii+155. MR 597091, DOI 10.1090/memo/0238
  • Günter Scheja and Uwe Storch, Differentielle Eigenschaften der Lokalisierungen analytischer Algebren, Math. Ann. 197 (1972), 137–170 (German). MR 306172, DOI 10.1007/BF01419591
  • A. Yu. Vaĭntrob, Deformations of complex structures on supermanifolds, Funktsional. Anal. i Prilozhen. 18 (1984), no. 2, 59–60 (Russian). MR 745703
  • —, Deformations of complex structures on supermanifolds, Reports of the Dept. of Math. Univ. Stockholm, 1988.
Similar Articles
Bibliographic Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 330 (1992), 1-40
  • MSC: Primary 32C11; Secondary 32G05, 32G13, 58A50
  • DOI: https://doi.org/10.1090/S0002-9947-1992-1069748-2
  • MathSciNet review: 1069748