{"paper":{"title":"Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Victor V. Batyrev","submitted_at":"1993-10-05T21:22:35Z","abstract_excerpt":"We consider families ${\\cal F}(\\Delta)$ consisting of complex $(n-1)$-dimensional projective algebraic compactifications of $\\Delta$-regular affine hypersurfaces $Z_f$ defined by Laurent polynomials $f$ with a fixed $n$-dimensional Newton polyhedron $\\Delta$ in $n$-dimensional algebraic torus ${\\bf T} =({\\bf C}^*)^n$. If the family ${\\cal F}(\\Delta)$ defined by a Newton polyhedron $\\Delta$ consists of $(n-1)$-dimensional Calabi-Yau varieties, then the dual, or polar, polyhedron $\\Delta^*$ in the dual space defines another family ${\\cal F}(\\Delta^*)$ of Calabi-Yau varieties, so that we obtain t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9310003","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/alg-geom/9310003/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}