{"paper":{"title":"$L^2$ and intersection cohomologies for the reductive representation of the fundamental groups of quasiprojective manifolds with unipotent local monodromy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Kang Zuo, Xuanming Ye","submitted_at":"2011-11-16T14:56:51Z","abstract_excerpt":"Let $X$ be a projective manifold, and $D$ be a normal crossing divisor of $X$. By Jost-Zuo's theorem that if we have a reductive representation $\\rho$ of the fundamental group $\\pi_{1}(X^{*})$ with unipotent local monodromy, where $X^*=X-D$, then there exists a tame pluriharmonic metric $h$ on the flat bundle $\\mathcal V$ associated to the local system $\\mathbb V$ obtain from $\\rho$ over $X^*$. Therefore, we get a harmonic bundle $(E, \\theta, h)$, where $\\theta$ is the Higgs field, i.e. a holomorphic section of $End(E)\\otimes\\Omega^{1,0}_{X^*}$ satisfying $\\theta^2=0$.\n  In this paper, we stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3825","kind":"arxiv","version":3},"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"}