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PRELIMINARIES CHAPTER A Algebra
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According algebraic algebraic set analytic germ analytic set analytic space analytic subset analytically constructible assume atlas biholomorphic bounded called Chapter chart closed coefficients compact condition connected Consequently Consider constant dimension contains continuous convergent coordinate system corollary covering decomposition defined denote dense domain element equal equivalent exists extension fact field finite follows function f germ graph hence holomorphic function holomorphic mapping homeomorphism ideal implies integral intersection inverse irreducible isomorphism lemma linear locally locally analytic manifold mapping f maximal means module Moreover multiplicity n-dimensional natural projection neighbourhood of zero non-zero normal Note Obviously open neighbourhood particular polynomial precisely PROOF proper proposition prove rank regular REMARK representative respectively restriction ring satisfies sequence simple components structure submanifold subspace sufficiently Suppose theorem true union unique vector space zero divisor