{"paper":{"title":"Symmetric products of a real curve and the moduli space of Higgs bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.DG"],"primary_cat":"math.SG","authors_text":"Thomas John Baird","submitted_at":"2016-11-29T14:05:48Z","abstract_excerpt":"Consider a Riemann surface $X$ of genus $g \\geq 2$ equipped with an antiholomorphic involution $\\tau$. This induces a natural involution on the moduli space $M(r,d)$ of semistable Higgs bundles of rank $r$ and degree $d$. If $D$ is a divisor such that $\\tau(D) = D$, this restricts to an involution on the moduli space $M(r,D)$ of semistable Higgs bundles of rank $r$ with fixed determinant $\\mathcal{O}(D)$ and trace-free Higgs field. The fixed point sets of these involutions $M(r,d)^{\\tau}$ and $M(r,D)^{\\tau}$ are $(A,A,B)$-branes introduced by Baraglia-Schaposnik. In this paper, we derive formu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09636","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"}