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Analytic geometry of complex superspaces


Authors: H. Flenner and D. Sundararaman
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
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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.


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  • [A$ _{1}$] M. Artin, On the solutions of analytic equations, Invent. Math. 5 (1968), 277-291. MR 0232018 (38:344)
  • [A$ _{2}$] M. Artin, Algebraization of formal moduli. I, Global Analysis, University of Tokyo Press, 1969, pp. 21-71. MR 0260746 (41:5369)
  • [A$ _{3}$] M. Artin, Versal deformations and algebraic stacks, Invent. Math. 27 (1974), 165-189. MR 0399094 (53:2945)
  • [Be] F. A. Berezin, Introduction to superanalysis (A. A. Kirilov, ed.), Reidel, 1987. MR 914369 (89b:58006)
  • [Bi$ _{1}$] J. Bingener, Über formale komplexe Räume, Manuscripta Math. 24 (1978), 253-293. MR 0492367 (58:11493)
  • [Bi$ _{2}$] -, Darstellbarkeitskriterien für analytische Funktoren, Ann. Sci. École Norm. Sup. (4) 13 (1980), 317-347. MR 597743 (82i:32047)
  • [Bi$ _{3}$] -, Offenheit der Versalität in der analytischen Geometrie, Math. Z. 173 (1980), 241-289. MR 592373 (82h:32025)
  • [Bi-Ko] J. Bingener and S. Kosarew, Lokale Modulräume in der analytischen Geometrie, Vieweg, Braunschweig.
  • [De] P. Deligne, Letter to D. Sundararaman, April 7, 1987.
  • [Do] A. Douady, Le problème des modules pour les sous espaces analytiques compacts d'un espace analytique donne, Ann. Inst. Fourier (Grenoble) 16 (1966), 1-95. MR 0203082 (34:2940)
  • [F$ _{1}$] H. Flenner, Deformationen holomorpher Abbildungen, Habilitationsschrift, Osnabrück, 1978.
  • [F$ _{2}$] -, Eine Bemerkung über relative Ext-Garben, Math. Ann. 258 (1981), 175-182. MR 641823 (83i:32019)
  • [F$ _{3}$] -, Ein Kriterium für die Offenheit der Versalität, Math. Z. 178 (1981), 449-473. MR 638811 (83e:32028)
  • [Fr] J. Frisch, Aplatissement en géométrie analytique, Ann Sci. École Norm. Sup. (4), 1 (1968), 305-312. MR 0236421 (38:4717)
  • [Gra$ _{1}$] H. Grauert, Der Satz von Kuranishi für kompakte komplexe Räume, Invent. Math. 25 (1974), 107-142. MR 0346194 (49:10920)
  • [Gra$ _{2}$] -, On meromorphic equivalence relations (Proc. Conf. in honor of W. Stoll), Aspects of Math. E9 (1986), 115-147. MR 859195 (88b:32023)
  • [Gro] A. Grothendieck, Techniques de construction en géométrie analytique. $ {\text{I}} - {\text{X}}$, Séminaire Cartan, 1960, 1962.
  • [Ha] R. Hartshorne, Residues and duality, Lecture Notes in Math., vol. 20, Springer-Verlag, Berlin-Heidelberg-New York, 1966. MR 0222093 (36:5145)
  • [Ki] R. Kiehl, Äquivalenzrelationen in analytischen Räumen, Math Z. 105 (1968), 1-20. MR 0232964 (38:1287)
  • [Ko-Ok] S. Kosarew and C. Okonek, Global moduli spaces and simple holomorphic bundles, Mathematica Gottingensis, Heft 10, 1987.
  • [Ku] M. Kuranishi, New proof for the existence of locally complete families of complex structures, Proc. Conf. Complex Analysis (Minneapolis 1964), Springer-Verlag, 1965, pp. 142-154. MR 0176496 (31:768)
  • [L] D. A. Leítes, Introduction to the theory of supermanifolds, Russian Math. Surveys 35 (1980), 1-64. MR 565567 (81j:58003)
  • [Ma$ _{1}$] Yu. I. Manin, New dimensions in geometry, Lecture Notes in Math., vol. 1111, Springer-Verlag, Berlin and New York, 1985, pp. 59-99. MR 797416 (87j:14030)
  • [Ma$ _{2}$] -, Gauge field theory and complex geometry, Grundlehren der Math., 289, Springer-Verlag, 1988. MR 954833 (89d:32001)
  • [Pa] V. P. Palamodov, Deformations of complex spaces, Russian Math. Surveys 31 (1984), 119-171. MR 0508121 (58:22671)
  • [Po] G. Pourcin, Théorèmes de Douady au-dessus de $ S$, Ann. Scuola Norm. Sup. Pisa C. Sci. (4) 23 (1969), 451-459. MR 0257402 (41:2053)
  • [Ri] R. S. Rim, Formal deformation theory, Groupes de Monodromie en Géométrie Algébrique (SGA7I), expose VI, Lecture Notes in Math., vol. 288, Springer-Verlag, Berlin and New York, 1972.
  • [RR] J. P. Ramis and G. Ruget, Complexe dualisant et théorèmes de dualité en géométrie analytique complexe, Inst. Hautes Études Sci. Publ. Math. 38 (1971), 77-91. MR 0279338 (43:5060)
  • [Sch] M. Schlessinger, Functors of Artin rings, Trans. Amer. Math. Soc. 130 (1968), 208-222. MR 0217093 (36:184)
  • [Schu$ _{1}$] H. W. Schuster, Formale Deformationstheorien, Habilitationsschrift, München, 1971.
  • [Schu$ _{2}$] -, Infinitesimale Erweiterungen komplexer Räume, Comment. Math. Helv. 45 (1970), 265-286. MR 0276496 (43:2243)
  • [SIT] Y. T. Siu and G. Trautmann, Deformations of coherent analytic sheaves with compact supports, Mem. Amer. Math. Soc., No. 238 (1981). MR 597091 (82c:32023)
  • [SS] G. Scheja and U. Storch, Differentielle Eigenschaften der Lokalisierungen analytischer Algebren, Math. Ann. 197 (1972), 137-170. MR 0306172 (46:5299)
  • [W$ _{1}$] A. Yu. Weintrob, Deformations of complex structures on supermanifolds, Functional Anal. Appl. 18 (1984), 59-60. MR 745703 (85k:32041)
  • [W$ _{2}$] -, Deformations of complex structures on supermanifolds, Reports of the Dept. of Math. Univ. Stockholm, 1988.

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DOI: https://doi.org/10.1090/S0002-9947-1992-1069748-2
Article copyright: © Copyright 1992 American Mathematical Society

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