On multiplicities of graded sequences of ideals

Details On multiplicities of graded sequences of ideals On multiplicities of graded sequences of ideals

2002-03-22

arxiv.org/abs/math/0203235v1

J. Algebra 256 (2002), 229-249.

Mathematics

Commutative Algebra

AMS-LaTeX, 21 pages

Scientific paper

We generalize a result of Ein-Lazarsfeld-Smith (math.AG/0202303), proving that for an arbitrary sequence of zero-dimensional ideals, the multiplicity of the sequence is equal with its volume. This is done using a deformation to monomial ideals. As a consequence of our result, we obtain a formula which computes the multiplicity of an ideal I in terms of the multiplicities of the initial monomial ideals of the powers I^m. We use this to give a new proof of the inequality between multiplicity and the log canonical threshold due to de Fernex, Ein and the author.

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