{"paper":{"title":"Rank two nilpotent co-Higgs sheaves on complex surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SG"],"primary_cat":"math.AG","authors_text":"Maur\\'icio Corr\\^ea","submitted_at":"2015-01-24T14:21:50Z","abstract_excerpt":"Let $(\\mathcal{E}, \\phi)$ be a rank two co-Higgs vector bundles on a K\\\"ahler compact surface $X$ with $\\phi\\in H^0(X,End(\\mathcal{E})\\otimes T_X)$ nilpotent. If $(\\mathcal{E}, \\phi)$ is semi-stable, then one of the following holds up to finite \\' etale cover:\n  $i)$ $X$ is uniruled.\n  $ii)$ $X$ is a torus and $(\\mathcal{E}, \\phi)$ is strictly semi-stable.\n  $iii)$ $X$ is a properly elliptic surface and $(\\mathcal{E}, \\phi)$ is strictly semi-stable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06045","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"}