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Titlebook: Complex Analytic Sets; E. M. Chirka Book 1989 Kluwer Academic Publishers 1989 Complex analysis.Dimension.Divisor.algebraic varieties

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Fundamentals of the Theory of Analytic Sets, U.: |z.| < r, counted with multiplicities. Then f can, in a certain neighborhood U = U’ × U. ⊂ V of the coordinate origin in ℂ., be represented in the form . where the functions c.(z’) are holomorphic in U’, while ϕ is holoniorphic and zero free in U.
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Tangent Cones and Intersection Theory,ne with vertex 0 since if ν ∈ .(., .), then .ν also belongs to .(., .) for all . ≥ 0. Geometrically the cone .(., .) is the set of limit positions of secants of . passing through .; it is the set of limit points of the family of sets .(. − .) = {.(. − .):. ∈ .} as .→∞. If . ∉ Ē then, by definition, the set . (., .) is empty.
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Tangent Cones and Intersection Theory,uch that . → . and . (. − .) → ν as .→ ∞. The set of all such tangent vectors is denoted by .(., .) and is called the . to . at .. This really is a cone with vertex 0 since if ν ∈ .(., .), then .ν also belongs to .(., .) for all . ≥ 0. Geometrically the cone .(., .) is the set of limit positions of
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0169-6378 in the purely algebraic language of ideals in commutative algebras..In the present book I have tried to eliminate this noncorrespondence and to give a geometri978-94-010-7565-7978-94-009-2366-9Series ISSN 0169-6378
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Metrical Properties of Analytic Sets,ally define in .Ω the operation of multiplication by a complex number ((. + .). = . +.), and complex conjugation Σ{.(∂/∂.)+.(∂/∂.) ↦ Σ{.(∂/∂.)−.(∂/∂.) (in .Ω the operator Σ.(∂/∂.) ↦ Σ̄.(∂/∂.) corresponds to it; do not confuse it with the corresponding operation in ℂ.Ω!). Hermiticity of .(.,.′) means
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