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EIN, LAZARSFELD, SMITH, AND VAROLIN coherent sheaves of ideals, and it is well-known that lct(A;As c grows larger, the ideals J X , c • A decrease, and the idea is simply to look at those (necessarily rational) values of c at which their stalks at x jump. Specifically, it is elementary that there is an increasing discrete sequencefor every i. (Here we agree by convention that J X , 0Definition. The rational numbers ξ i (A; x) are the jumping coefficients or jumping numbers of A at x. We say that ξ is a jumping coefficient of A on X if it is a jumping number of A at some point x ∈ X.Given an ideal sheaf a ⊆ O X , the jumping numbers ξ i (a; x) ∈ Q are defined similarly using the multiplier ideals J X , c • a = J X , a c .We begin in Section 1 by establishing some formal properties of these numbers:Proposition A. Let A be an effective integral divisor on X passing through x.(i). The collection of all jumping numbers of A is periodic with period 1. Specifically, ξ is a jumping number for A at x if and only if (1 + ξ) is. (ii). The jumping numbers of A satisfy the inequality (1) ξ i+1 (A; x) ≤ ξ i (A; x) + ξ 1 (A; x)for every i ≥ 1. 40 (1983), 641-652.

We characterize bounded and compact Toeplitz operators defined on generalized Bargmann-Fock spaces.

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We consider stable manifolds of a holomorphic diffeomorphism of a complex manifold. Using a conjugation of the dynamics to a (non-stationary) polynomial normal form, we show that typical stable manifolds are biholomorphic to complex Euclidean space.Comment: 17 pages. Revised version. To appear in Inv. Mat