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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
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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.

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Keywords: Representable functor, compact complex space, hyperbolic space, complex fibre space
Article copyright: © Copyright 1975 American Mathematical Society