Abstract
Abstract This paper is devoted to the study of the asymptotics of Monge–Ampère volumes of direct images associated with high tensor powers of an ample line bundle. We study the leading term of this asymptotics and provide a classification of bundles saturating the topological bound of Demailly. In the special case of high symmetric powers of ample vector bundles, this provides a characterization of those admitting projectively flat Hermitian structures.
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