Growth of balls of holomorphic sections on projective toric varieties

Abstract

Let [Formula: see text] be an equivariant line bundle which is big and nef on a complex projective nonsingular toric variety [Formula: see text]. Given a continuous toric metric [Formula: see text] on [Formula: see text], we define the energy at equilibrium of [Formula: see text] where [Formula: see text] is the weight of the metrized toric divisor [Formula: see text]. We show that this energy describes the asymptotic behavior as [Formula: see text] of the volume of the [Formula: see text]-norm unit ball induced by [Formula: see text] on the space of global holomorphic sections [Formula: see text].