{"paper":{"title":"On monodromy representation of period integrals associated to an algebraic curve with bi-degree (2,2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Susumu Tanab\\'e","submitted_at":"2017-12-01T22:25:11Z","abstract_excerpt":"We study a problem related to Kontsevich's homological mirror symmetry conjecture for the case of a generic curve $\\cal Y$ with bi-degree (2,2) in a product of projective lines ${\\Bbb P}^{1} \\times {\\Bbb P}^{1}$. We calculate two differenent monodromy representations of period integrals for the affine variety ${\\cal X}^{(2,2)}$ obtained by the dual polyhedron mirror variety construction from $\\cal Y$. The first method that gives a full representation of the fundamental group of the complement to singular loci relies on the generalised Picard-Lefschetz theorem. The second method uses the analyt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00505","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"}