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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A representable functor theorem for compact analytic spaces and applications
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by Andrew J. Sommese PDF
Proc. Amer. Math. Soc. 52 (1975), 11-17 Request permission

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
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  • Jean-Pierre Serre, Prolongement de faisceaux analytiques cohérents, Ann. Inst. Fourier (Grenoble) 16 (1966), no. fasc. 1, 363–374 (French). MR 212214
  • A. J. Sommese, Algebraic properties of the period mapping, Thesis, Princeton University, Princeton, N. J., 1973.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 11-17
  • MSC: Primary 32J99; Secondary 32C15
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0425190-1
  • MathSciNet review: 0425190