{"paper":{"title":"Yang-Mills-Higgs connections on Calabi-Yau manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Alessio Lo Giudice, Beatriz Gra\\~na Otero, Indranil Biswas, Ugo Bruzzo","submitted_at":"2014-12-24T19:19:13Z","abstract_excerpt":"Let $X$ be a compact connected K\\\"ahler--Einstein manifold with $c_1(TX)\\, \\geq\\, 0$. If there is a semistable Higgs vector bundle $(E\\,,\\theta)$ on $X$ with $\\theta\\,\\not=\\,0$, then we show that $c_1(TX)=0$, any $X$ satisfying this condition is called a Calabi--Yau manifold, and it admits a Ricci--flat K\\\"ahler form \\cite{Ya}. Let $(E\\,,\\theta)$ be a polystable Higgs vector bundle on a compact Ricci--flat K\\\"ahler manifold $X$. Let $h$ be an Hermitian structure on $E$ satisfying the Yang--Mills--Higgs equation for $(E\\,,\\theta)$. We prove that $h$ also satisfies the Yang--Mills--Higgs equatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7738","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"}