{"paper":{"title":"On the approximation of positive closed currents on compact Kaehler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.CV","authors_text":"Dan Coman, George Marinescu","submitted_at":"2013-02-01T21:12:30Z","abstract_excerpt":"Let $L$ be a holomorphic line bundle over a compact K\\\"ahler manifold $X$ endowed with a singular Hermitian metric $h$ with curvature current $c_1(L,h)\\geq0$. In certain cases when the wedge product $c_1(L,h)^k$ is a well defined current for some positive integer $k\\leq\\dim X$, we prove that $c_1(L,h)^k$ can be approximated by averages of currents of integration over the common zero sets of $k$-tuples of holomorphic sections over $X$ of the high powers $L^p:=L^{\\otimes p}$.\n  In the second part of the paper we study the convergence of the Fubini-Study currents and the equidistribution of zeros"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0292","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}