{ "id": "2010.01839", "version": "v1", "published": "2020-10-05T07:51:10.000Z", "updated": "2020-10-05T07:51:10.000Z", "title": "On Monge-Amp{รจ}re volumes of direct images", "authors": [ "Siarhei Finski" ], "categories": [ "math.DG", "math.SP" ], "abstract": "This paper is devoted to the study of the asymptotics of Monge-Amp{\\`e}re 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.", "revisions": [ { "version": "v1", "updated": "2020-10-05T07:51:10.000Z" } ], "analyses": { "keywords": [ "direct images", "ample line bundle", "ample vector bundles", "bundles admitting projectively flat hermitian", "high tensor powers" ], "note": { "typesetting": "TeX", "pages": 0, "language": "en", "license": "arXiv", "status": "editable" } } }