{"paper":{"title":"Variations of Hodge structures for hypergeometric differential operators and parabolic Higgs bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Roman Fedorov","submitted_at":"2015-05-07T13:52:05Z","abstract_excerpt":"Consider the holomorphic bundle with connection on $\\mathbb P^1-\\{0,1,\\infty\\}$ corresponding to the regular hypergeometric differential operator \\[\n  \\prod_{j=1}^h(D-\\alpha_j)-z\\prod_{j=1}^h(D-\\beta_j), \\qquad D=z\\frac{d}{dz}. \\] If the numbers $\\alpha_i$ and $\\beta_j$ are real and for all $i$ and $j$ the number $\\alpha_i-\\beta_j$ is not integer, then the bundle with connection is known to underlie a complex polarizable variation of Hodge structures. We calculate some Hodge invariants for this variation, in particular, the Hodge numbers. From this we derive a conjecture of Corti and Golyshev."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01704","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"}