Pluripotential Theory and Convex Bodies

Abstract

In their seminal paper, Berman and Boucksom exploited ideas from complex geometry to analyze asymptotics of spaces of holomorphic sections of tensor powers of certain line bundles $L$ over compact, complex manifolds as the power grows. This yielded results on weighted polynomial spaces in weighted pluripotential theory in ${\mathbb{C}}^d$. Here, motivated from Bayraktar's recent paper, we work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body in $({\mathbb{R}}^{+}{)}^d$. These classes of polynomials need not occur as sections of tensor powers of a line bundle $L$ over a compact, complex manifold. We follow the approach in Berman and Boucksom's work to recover analogous results.

References in corpus (2)

• Zero distribution of random sparse polynomials
• Bergman kernels for weighted polynomials and weighted equilibrium measures of C^n

Cited by in corpus (7)

• Log-concavity of volume and complex Monge-Ampère equations with prescribed singularity
• Pluripotential Theory and Convex Bodies: A Siciak-Zaharjuta theorem
• Transfinite diameter with generalized polynomial degree
• The Extremal Function for the Complex Ball for Generalized Notions of Degree and Multivariate Polynomial Approximation
• C-transfinite diameter
• Correction/Addendum to "The Extremal Function for the Complex Ball for Generalized Notions of Degree and Multivariate Polynomial Approximation"
• Polynomials associated to non-convex bodies