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arXiv · 2010.01839

On Monge-Amp\`ere volumes of direct images

Siarhei Finski
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Abstract

This paper is devoted to the study of the asymptotics of Monge-Amp\`ere 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 vector bundles admitting projectively flat Hermitian structures.

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Siarhei Finski. 2020-10-05. On Monge-Amp\`ere volumes of direct images. https://doi.org/10.1093/imrn%2Frnab058

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