{"paper":{"title":"A vanishing theorem for co-Higgs bundles on the moduli space of bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AG","authors_text":"Indranil Biswas, Steven Rayan","submitted_at":"2016-09-13T01:54:55Z","abstract_excerpt":"We consider smooth moduli spaces of semistable vector bundles of fixed rank and determinant on a compact Riemann surface $X$ of genus at least $3$. The choice of a Poincar\\'e bundle for such a moduli space $M$ induces an isomorphism between $X$ and a component of the moduli space of semistable sheaves over $M$. We prove that $h^0(M, \\text{End}({\\mathcal E})\\otimes TM)= 1$ for a vector bundle $\\mathcal E$ on $M$ coming from this component. Furthermore, there are no nonzero integrable co-Higgs fields on $\\mathcal E$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03655","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"}