Asymptotic multiplicities and Monge-Ampère masses (with an appendix by Sébastien Boucksom)

Abstract

Ein, Lazarsfeld and Smith asked whether `equality' holds between two Samuel type asymptotic multiplicities for a graded system of zero-dimensional ideals on a smooth complex variety. We find a connection of this question to complex analysis by showing that the `equality' is equivalent to a particular case of Demailly's strong continuity property on the convergence of residual Monge-Ampère masses under approximation of plurisubharmonic functions. On the other hand, in an appendix of this paper, Sébastien Boucksom gives an algebraic proof of the `equality' in general, using the intersection theory of b-divisors. We then use these to show that Demailly's strong continuity holds for a new important class of plurisubharmonic functions.

arXiv commentSome changes in Sec. 2,3,5, to appear in Math. Ann