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On multiplicities of graded sequences of ideals
Get PDFWe 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.Comment: AMS-LaTeX, 21 page
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