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Titlebook: Equimultiplicity and Blowing Up; An Algebraic Study Manfred Herrmann,Ulrich Orbanz,Shin Ikeda Book 1988 Springer-Verlag Berlin Heidelberg 1

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Review of Multiplicity Theory,In this chapter we collect all the basic facts about multiplicities, Hilbert functions and reductions of ideals. At the same time we will introduce the notations to be used throughout the book.
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978-3-642-64803-8Springer-Verlag Berlin Heidelberg 1988
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Local Cohomology and Duality of Graded Rings,most results in this chapter hold for any noetherian ring or any noetherian local ring R by regarding R as a graded ring with the trivial grading R. = R and R. = 0 for n ≠ 0. On the other hand our theory of graded rings can be extended to any ..-graded rings as Goto and Watanabe have done in [17].
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Petr Kaplický,Josef Málek,Jana Staráves. Finally for inequalities of Hilbert functions under blowing up other centers one has to apply this semicontinuity. The last Section 32 is related to equisingularity theory via flat families. As before (R,m,k) is again a noetherian local ring and I a proper ideal of R.
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https://doi.org/10.1007/978-1-4614-2236-5ohomology, see main Theorem (44.1). Then we ask this question for Rees rings of equimultiple ideals I, in particular of m-primary ideals and of ideals q and q., where q is generated by a system of parameters.
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