{"paper":{"title":"Higgs bundles and representation spaces associated to morphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Carlos Florentino, Indranil Biswas","submitted_at":"2015-07-16T13:40:29Z","abstract_excerpt":"Let $G$ be a connected reductive affine algebraic group defined over the complex numbers, and $K\\subset G$ be a maximal compact subgroup. Let $X , Y$ be irreducible smooth complex projective varieties and $f: X \\rightarrow Y$ an algebraic morphism, such that $\\pi_1(Y)$ is virtually nilpotent and the homomorphism $f_* : \\pi_1(X) \\rightarrow\\pi_1(Y)$ is surjective. Define $$ {\\mathcal R }^f(\\pi_1(X),\\, G)\\,=\\, \\{\\rho\\, \\in\\, \\text{Hom}(\\pi_1(X),\\, G)\\, \\mid\\, A\\circ\\rho \\ \\text{ factors through }~ f_*\\}\\, , $$ $$ {\\mathcal R }^f(\\pi_1(X),\\, K)\\,=\\, \\{\\rho\\, \\in\\, \\text{Hom}(\\pi_1(X),\\, K)\\, \\mid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04568","kind":"arxiv","version":1},"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"}