Equimultiplicity and Blowing Up by Manfred Herrmann, Shin Ikeda, Ulrich Orbanz (Paperback, 2011)

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I - Review of Multiplicity Theory. - 1 The multiplicity symbol. - 2 Hilbert functions. - 3 Generalized multiplicities and Hilbert functions. - 4 Reductions and integral closure of ideals. - 5 Faithfully flat extensions.