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- W105223735 abstract "In the preceding chapter we have investigated the topological space X(ℂ) connected with an arbitrary algebraic manifold X defined over the field of complex numbers ℂ. The example of smooth projective curves shows to what extent this space characterizes the variety X. We have shown that in this case the only invariant of X(ℂ) is the genus of X. We can say, therefore, that the genus is the only topological invariant of a projective curve. Undoubtedly, the genus is a most important invariant of an algebraic curve, however, it does not determine the curve by any means. We have seen in Ch. III, § 5.6, that there exist very many non-isomorphic curves of one and the same genus. The connection between a variety X and the space X(ℂ) for varieties of higher dimensions bears a similar character." @default.
- W105223735 created "2016-06-24" @default.
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- W105223735 date "1977-01-01" @default.
- W105223735 modified "2023-09-27" @default.
- W105223735 title "Complex Analytic Manifolds" @default.
- W105223735 doi "https://doi.org/10.1007/978-3-642-96200-4_8" @default.
- W105223735 hasPublicationYear "1977" @default.
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