This two volume work on Positivity in Algebraic Geometry contains a contemporary account
of a body of work in complex algebraic geometry loosely centered around the theme of …

In this paper the asymptotic behavior of the Castelnuovo $ ndash; Mumford regularity of
powers of a homogeneous ideal I is studied. It is shown that there is a linear bound for the …

The Dynamical Mordell-Lang Conjecture is an analogue of the classical Mordell-Lang
conjecture in the context of arithmetic dynamics. It predicts the behavior of the orbit of a point …

Fix a rank one valuation ν centered at a smooth point x on an algebraic variety over a field of
characteristic zero. Assume that ν is Abhyankar, that is, that its rational rank plus its …

We prove a dynamical version of the Mordell-Lang conjecture for étale endomorphisms of
quasiprojective varieties. We use $ p $-adic methods inspired by the work of Skolem …

We find simple necessary and sufficient conditions on a local ring R of dimension d for the
limit lim n→∞⁡ ℓ R (R/I n) nd to exist whenever {I n} is a graded family of m R-primary …

La théorie des corps d'Okounkov, développée indépendamment par Lazarsfeld et Mustata
[LM09] et par Kaveh et Khovanskii [KK09], systématise une construction duea Okounkov …

Regularity....................................................... 1 1.2 A Lemma from Homological Algebra and the
Equivalenceof the Definitions................................................ 3 1.3 Other Definitions and Further …

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 …

We study the orbits of a polynomial f∈ C [X], namely, the sets {α, f (α), f (f (α)),…} with α∈ C.
We prove that if two nonlinear complex polynomials f, g have orbits with infinite intersection …