We prove that limits of multiplicities associated to graded families of ideals exist under very
general conditions. Most of our results hold for analytically unramified equicharacteristic …

This paper is on graded families of ideals and filtrations and associated asymptotic
multiplicities. We prove some new results, including a general Minkowski formula for limits …

We generalize a result from [L. Ein, et al., math. AG/0202303], proving that for an arbitrary
graded sequence of zero-dimensional ideals, the multiplicity of the sequence is equal to its …

If R is a local ring of dimension n, of a smooth complex variety, and if I is a zero dimensional
ideal in R, then we prove that e (I)\geq n^ n/lc (I)^ n. Here e (I) is the Samuel multiplicity …

Let (R; m) be a local ring of Krull dimension d and I⊆ R be an ideal with analytic spread d.
We show that the j-multiplicity of I is determined by the Rees valuations of I centered on m …

The depth of the associated graded ring of the powers of an ideal I of a local ring R is
studied. It is proved that the depth of the associated graded ring of In is asymptotically …

We prove a uniform bound on the growth of symbolic powers of arbitrary (not necessarily
radical) ideals in arbitrary (not necessarily excellent) regular rings of all characteristics. This …

We give general bounds for the reduction numbers of ideals in arbitrary Noetherian rings
and multiplicity-dependent bounds for m-primary ideals in a Noetherian local ring (R, m). In …

Let R be a Noetherian ring of positive characteristic p. For every ideal a in R, and for every
ideal J whose radical contains a, one can define asymptotic invariants that measure the …

Ein, Lazarsfeld, and Smith proved in [ELS] the following uniform behavior of symbolic
powers of ideals in affine regular rings of equal characteristic 0: If h is the largest height of …