Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Moišezon spaces and positive coherent sheaves


Author: Joshua H. Rabinowitz
Journal: Proc. Amer. Math. Soc. 71 (1978), 237-240
MSC: Primary 32J20
MathSciNet review: 0486667
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In recent papers of Grauert and Riemenschneider, attempts have been made to generalize Kodaira's embedding theorem to a characterization of Moišezon spaces. In this paper, we define a torsion-free coherent analytic sheaf of generic fiber dimension one as positive if its monoidal transform is positive. We prove: a normal irreducible compact complex space is Moišezon if and only if it carries a positive coherent sheaf of generic fiber dimension one.


References [Enhancements On Off] (What's this?)

  • [1] G. Fischer, Lineare Faserraume und koharente Modulgarben über komplexen Raumen, Arch. Math. 18 (1967), 609-617. MR 0220972 (36:4024)
  • [2] -, Complex analytic geometry, Lecture Notes in Math., vol. 538, Springer-Verlag, Berlin and New York, 1976. MR 0430286 (55:3291)
  • [3] H. Grauert, Über Modifikationen und exceptionelle analytische Mengen, Math. Ann. 146 (1962), 331-368. MR 0137127 (25:583)
  • [4] H. Grauert and O. Riemenschneider, Verschwindungssatze für analytische Kohomologiegruppen auf komplexen Raumen, Invent. Math. 11 (1970), 263-292. MR 0302938 (46:2081)
  • [5] P. Griffiths, Hermitian differential geometry, Chern classes, and positive vector bundles, Global Analysis (Papers in Honor of K. Kodaira), Univ. of Tokyo Press, Tokyo; Princeton Univ. Press, Princeton, N. J., 1969, pp. 185-251. MR 0258070 (41:2717)
  • [6] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109-326. MR 0199184 (33:7333)
  • [7] B. G. Moišezon, On n-dimensional compact varieties with n algebraically independent meromorphic functions. I, II, III, Izv. Akad. Nauk SSSR Ser. Mat. 30 (1966), 133-174; 345-386; 621-656; English transl., Amer. Math. Soc. Transl. (2) 63 (1967), 51-177.
  • [8] -, Resolution theorems for compact complex spaces with a sufficiently large field of meromorphic functions, Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 1385-1414; English transl., Math. USSR-Izv. 1 (1967), 1331-1356. MR 0222917 (36:5967)
  • [9] -, Modifications of complex varieties and the Chow lemma, Classification of Algebraic Varieties and Compact Complex Manifolds, edited by H. Popp, Lecture Notes in Math., vol. 412, Springer-Verlag, Berlin and New York, 1974, pp. 133-139. MR 0369746 (51:5978)
  • [10] J. Morrow and H. Rossi, Some theorems of algebraicity for complex spaces, J. Math. Soc. Japan (2) 27 (1975), 167-183. MR 0407326 (53:11102)
  • [11] O. Riemenschneider, Characterizing Moišezon spaces by almost positive coherent analytic sheaves, Math. Z. 123 (1971), 263-284. MR 0294714 (45:3782)
  • [12] -, A Generalization of Kodaira's embedding theorem, Math. Ann. 200 (1973), 99-102. MR 0326009 (48:4355)
  • [13] H. Rossi, Picard variety of an isolated singular point, Rice Univ. Studies 54 (1968), 63-73. MR 0244517 (39:5831)
  • [14] R. O. Wells, Jr., Moišezon spaces and the Kodaira embedding theorem, Value Distribution Theory, Part A, edited by R. O. Kujala and A. L. Vitter III, Dekker, New York, 1973, pp. 29-42. MR 0374499 (51:10699)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32J20

Retrieve articles in all journals with MSC: 32J20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0486667-9
Keywords: Moišezon space, coherent analytic sheaf, monoidal transformation, positive line bundle, Kodaira embedding theorem
Article copyright: © Copyright 1978 American Mathematical Society