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Complete varieties

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1358)

Abstract

An affine variety can be embedded in a projective variety, by a birational inclusion. Can a projective variety be embedded birationally in anything even bigger? The answer is no; there is a type of variety, called complete, which in our algebraic theory plays the same role as compact spaces do in the theory of topological spaces. These are “maximal” and projective varieties turn out to be complete.

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© 1988 Springer-Verlag Berlin Heidelberg

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Mumford, D. (1988). Complete varieties. In: The Red Book of Varieties and Schemes. Lecture Notes in Mathematics, vol 1358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21581-4_9

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  • DOI: https://doi.org/10.1007/978-3-662-21581-4_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50497-9

  • Online ISBN: 978-3-662-21581-4

  • eBook Packages: Springer Book Archive