Titlebook: Local Analytic Geometry; Basic Theory and App Theo Jong,Gerhard Pfister Textbook 2000 Springer Fachmedien Wiesbaden 2000 Algebraische Geome

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和平主义者

Plane Curve Singularities,rsection multiplicity of two (irreducible) plane curve singularities (., o) and (., o). This number can be calculated as follows. Consider the normalization ℂ{.} of .., and let (., o) be given by . = 0. Via the inclusion .. ∈ℂ{.}, we can consider at . as an element of ℂ{.}. Then the intersection mul

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Classification of Simple Hypersurface Singularities,acy Theorems. Let m be the maximal ideal of ℂ{..,... ,..}. A function / is called (right) .-determined if for all elements . with . ∈ m.. the functions / and . are right equivalent. In particular, a .-determined . is right equivalent to a polynomial of degree at most .. A function is called finitely

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Textbook 2000ll do in this book, as the "commutative algebra" one needs in local analytic geometry is somewhat more difficult: one has to cope with convergence questions. The most prominent and important example is the substitution of division with remainder. Its substitution in local analytic geometry is called

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0932-7134 (over an algebraically closed field). As one often reads in prefaces of int- ductory books on algebraic geometry, it is not so easy to develop the basics of algebraic geometry without a proper knowledge of commutative algebra. On the other hand, the commutative algebra one needs is quite difficult t

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Approximation Theorems, system of analytic equations has a formal solution (which is sometimes really not convergent) then we can find a convergent solution to this system. Even more, we can approximate the formal one by convergent ones up to a given order.

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Standard Bases,s regular of order . in ... For any . ∈ ℂ . we have a unique representation . with . a polynomial of degree less than .. From the uniqueness statement in the Weierstraß Division Theorem, it follows without difficulty that the remainder . only depends on the coset .) of (.). Of course, the remainder . depends on the choice of ...

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