Abstract
Let X be an equidimensional scheme of finite type over a perfect field k. Under these conditions, the multiplicity along points of X defines an upper semi-continuous function, say multX:X→N, which stratifies X into its locally closed level sets. We study this stratification, and the behavior of the multiplicity when blowing up at regular equimultiple centers. We also discuss a natural compatibility of these two concepts when X is replaced with its underlying reduced scheme. The main result in this paper is to show that, given a variety X, there is a well defined Rees algebra over X, naturally attached to maximum value of the multiplicity.
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