Lelong classes on toric varieties and a theorem of Siciak

TL;DR

This paper characterizes Lelong classes on toric varieties with ample line bundles, extending Siciak's approximation theorem, and provides a counterexample for non-ample cases.

Contribution

It generalizes Siciak's approximation theorem to toric manifolds with ample line bundles and explores the limitations when the line bundle is not ample.

Findings

Characterization of Lelong classes on toric manifolds with ample line bundles

Extension of Siciak's approximation theorem to this setting

Counterexample showing failure when the line bundle is not ample

Abstract

We characterize Lelong classes on a toric manifold with an ample torus invariant line bundle, generalizing an approximation theorem due to Siciak. We include a counterexample to the theorem when the line bundle is globally generated, but not ample.