Content and Subject Matter: This research monograph deals with two
main subjects, namely the notion of equimultiplicity and the
algebraic study of various graded rings in relation to blowing ups.
Both subjects are clearly motivated by their use in resolving
singularities of algebraic varieties, for which one of the main
tools consists in blowing up the variety along an equimultiple
subvariety. For equimultiplicity a unified and self-contained
treatment of earlier results of two of the authors is given,
establishing a notion of equimultiplicity for situations other than
the classical ones. For blowing up, new results are presented on
the connection with generalized Cohen-Macaulay rings. To keep this
part self-contained too, a section on local cohomology and local
duality for graded rings and modules is included with detailed
proofs. Finally, in an appendix, the notion of equimultiplicity for
complex analytic spaces is given a geometric interpretation and its
equivalence to the algebraic notion is explained. The book is
primarily addressed to specialists in the subject but the
self-contained and unified presentation of numerous earlier results
make it accessible to graduate students with basic knowledge in
commutative algebra.
General
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