{"work":{"id":"6da39747-5d6a-494d-a6fd-6de24bb15403","openalex_id":null,"doi":null,"arxiv_id":"alg-geom/9310003","raw_key":null,"title":"Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties","authors":null,"authors_text":"V","year":1993,"venue":"alg-geom","abstract":"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 the remarkable duality between two {\\em different families} of Calabi-Yau varieties. It is shown that the properties of this duality coincide with the properties of {\\em Mirror Symmetry} discovered by physicists for Calabi-Yau $3$-folds. Our method allows to construct many new examples of Calabi-Yau $3$-folds and new candidats for their mirrors which were previously unknown for physicists. We conjecture that there exists an isomorphism between two conformal field theories corresponding to Calabi-Yau varieties from two families ${\\cal F}(\\Delta)$ and ${\\cal F}(\\Delta^*)$.","external_url":"https://arxiv.org/abs/alg-geom/9310003","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-07-03T06:57:43.112294+00:00","pith_arxiv_id":"alg-geom/9310003","created_at":"2026-05-11T04:25:59.853821+00:00","updated_at":"2026-07-03T06:57:43.112294+00:00","title_quality_ok":true,"display_title":"Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties","render_title":"Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties"},"hub":{"state":{"work_id":"6da39747-5d6a-494d-a6fd-6de24bb15403","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":13,"external_cited_by_count":null,"distinct_field_count":3,"first_pith_cited_at":"2020-08-24T18:01:55+00:00","last_pith_cited_at":"2026-06-26T14:10:40+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-07-03T15:04:36.993511+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":3},{"context_role":"method","n":1}],"polarity_counts":[{"context_polarity":"background","n":3},{"context_polarity":"use_method","n":1}],"runs":{},"summary":{},"graph":{},"authors":[]}}