Partial pluricomplex energy and integrability exponents of plurisubharmonic functions

2 4 Fe b 20 05 VALUATIONS AND MULTIPLIER IDEALS

We present a new approach to the study of multiplier ideals in a local, two-dimensional setting. Our method allows us to deal with ideals, graded systems of ideals and plurisubharmonic functions in a unified way. Among the applications are a formula for the complex integrability exponent of a plurisubharmonic function in terms of Kiselman numbers, and a proof of the openness conjecture by Demai...

ar X iv : m at h / 04 06 10 9 v 1 [ m at h . C V ] 7 J un 2 00 4 VALUATIONS AND MULTIPLIER IDEALS

We present a new approach to the study of multiplier ideals in a local, two-dimensional setting. Our method allows us to deal with of ideals, graded systems of ideals and plurisubharmonic functions in a unified way. Among the applications are a formula for the complex integrability exponent of a plurisubharmonic function in terms of Kiselman numbers, and a proof of the “openness conjecture” by ...

Plurisubharmonic functions in calibrated geometry and q-convexity

Let (M,ω) be a Kähler manifold. An integrable function φ on M is called ω-plurisubharmonic if the current ddφ ∧ ω is positive. We prove that φ is ωplurisubharmonic if and only if φ is subharmonic on all q-dimensional complex subvarieties. We prove that a ωplurisubharmonic function is q-convex, and admits a local approximation by smooth, ω-plurisubharmonic functions. For any closed subvariety Z ...

Zeroes of Real-Analytic Functions, Critical Integrability Exponents, and Oscillatory Integrals

Convergence in Capacity of the Pluricomplex Green Function

In this paper we prove that if Ω is a bounded hyperconvex domain in C and if Ω 3 zj → ∂Ω, j → ∞, then the pluricomplex Green function gΩ(zj , ·) tends to 0 in capacity, as j →∞. A bounded open connected set Ω ⊂ Cn is called hyperconvex if there exists negative plurisubharmonic function ψ ∈ PSH(Ω) such that {z ∈ Ω : ψ(z) < c} ⊂⊂ Ω for all c < 0. Such ψ is called an exhaustion function for Ω. It ...