Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A representable functor theorem for compact analytic spaces and applications


Author: Andrew J. Sommese
Journal: Proc. Amer. Math. Soc. 52 (1975), 11-17
MSC: Primary 32J99; Secondary 32C15
MathSciNet review: 0425190
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the functor given by maps from a given compact analytic space $ X$ into elements of a category $ C$ of analytic spaces is representable by a compact element of $ C$ if and only if $ C$ is closed under finite products and the taking of compact subspaces. Various specific choices are considered. Of special interest is the category of compact hyperbolic spaces which gives rise to a birational invariant when applied to projective manifolds.


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

  • [1] Henri Cartan, Quotients of complex analytic spaces, Contributions to function theory (Internat. Colloq. Function Theory, Bombay, 1960) Tata Institute of Fundamental Research, Bombay, 1960, pp. 1–15. MR 0139769 (25 #3199)
  • [2] 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 0203082 (34 #2940)
  • [3] Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker, Inc., New York, 1970. MR 0277770 (43 #3503)
  • [4] Jean-Pierre Serre, Prolongement de faisceaux analytiques cohérents, Ann. Inst. Fourier (Grenoble) 16 (1966), no. fasc. 1, 363–374 (French). MR 0212214 (35 #3088)
  • [5] A. J. Sommese, Algebraic properties of the period mapping, Thesis, Princeton University, Princeton, N. J., 1973.
  • [6] K. Stein, On factorization of holomorphic mappings, Proc. Conf. Complex Analysis (Minneapolis, 1964) Springer, Berlin, 1965, pp. 1–7. MR 0178161 (31 #2419)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32J99, 32C15

Retrieve articles in all journals with MSC: 32J99, 32C15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0425190-1
PII: S 0002-9939(1975)0425190-1
Keywords: Representable functor, compact complex space, hyperbolic space, complex fibre space
Article copyright: © Copyright 1975 American Mathematical Society