{"paper":{"title":"Enhanced homotopy theory for period integrals of smooth projective hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AT","math.MP"],"primary_cat":"math.AG","authors_text":"Jae-Suk Park, Jeehoon Park","submitted_at":"2013-10-24T18:58:37Z","abstract_excerpt":"The goal of this paper is to reveal hidden structures on the singular cohomology and the Griffiths period integral of a smooth projective hypersurface in terms of BV(Batalin-Vilkovisky) algebras and homotopy Lie theory (so called, $L_\\infty$-homotopy theory).\n  Let $X_G$ be a smooth projective hypersurface in the complex projective space $\\mathbf{P}^n$ defined by a homogeneous polynomial $G(\\underline x)$ of degree $d \\geq 1$. Let $\\mathbb{H}=H^{n-1}_{\\operatorname{prim}}(X_G, \\mathbb{C})$ be the middle dimensional primitive cohomology of $X_G$. We explicitly construct a BV algebra $\\mathbf{B\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6710","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"}