Abstract
In this chapter we generalize some of the results of Chapter II to varieties of arbitrary dimension. Let us begin by putting into perspective some of the results of Chapter II. A curve C in ℂ2 or ℙ2(ℂ) defines a topological space, its topology being induced from that of ℂ2 or ℙ2(ℂ). If, in particular, C is non-singular, then it is a topological 2-manifold (cf. the discussion after Theorem 2.7 of Chapter I). In fact, it is actually an analytic manifold, in the sense that all the homeomorphisms ф β −>1 ○ фα of Definition 9.3 of Chapter II are analytic.
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© 1977 Springer- Verlag, New York Inc.
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Kendig, K. (1977). Varieties of arbitrary dimension. In: Elementary Algebraic Geometry. Graduate Texts in Mathematics, vol 44. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-6899-5_4
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DOI: https://doi.org/10.1007/978-1-4615-6899-5_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4615-6901-5
Online ISBN: 978-1-4615-6899-5
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