{"paper":{"title":"Parabolic degrees and Lyapunov exponents for hypergeometric local systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AG","authors_text":"Charles Fougeron","submitted_at":"2017-01-29T14:32:55Z","abstract_excerpt":"Consider the flat bundle on $\\mathrm{CP}^1 - \\{0,1,\\infty \\}$ corresponding to solutions of the hypergeometric differential equation $ \\prod_{i=1}^h (\\mathrm D - \\alpha_i) - z \\prod_{j=1}^h (\\mathrm D - \\beta_j) = 0$ where $\\mathrm D = z \\frac {d}{dz}$. For $\\alpha_i$ and $\\beta_j$ distinct real numbers, this bundle is known to underlie a complex polarized variation of Hodge structure. Setting the complete hyperbolic metric on $\\mathrm{CP}^1 - \\{0,1,\\infty \\}$, we associate $n$ Lyapunov exponents to this bundle. We compute the parabolic degrees of the holomorphic subbundles induced by the vari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08387","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"}