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| Autori principali: | , |
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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2403.07139 |
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| _version_ | 1866917517338869760 |
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| author | Berglund, Per Hübsch, Tristan |
| author_facet | Berglund, Per Hübsch, Tristan |
| contents | Standard toric geometry methods used to construct Calabi-Yau varieties may be extended to complete intersections in non-Fano varieties encoded by star triangulating non-convex polytopes. Similarly, mirror symmetry is conjectured to hold in terms of a transpolar duality generalizing the original construction of Batyrev and Borisov. The associated mirror pairs naturally include certain flip-folded, multi-layered multihedral objects, inclusively named VEX multitopes, and a correspondingly generalized transpolar duality. These self-overlaying VEX multitopes, long since known in pre-symplectic geometry, are found to correspond to certain non-algebraic but smooth toric spaces with Chern classes that satisfy the standard Todd-Hirzebruch identities. The computation of diffeomorphism invariants, including characteristic submanifold intersection numbers, corroborates their recent inclusion in the connected web of Calabi-Yau spaces and associated string compactifications: They arise together with the standard (Fano/reflexive polytope) constructions, within deformation families of generalized complete intersections in products of projective spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07139 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chern Characteristics and Todd-Hirzebruch Identities for Transpolar Pairs of Toric Spaces Berglund, Per Hübsch, Tristan High Energy Physics - Theory Algebraic Geometry Symplectic Geometry Standard toric geometry methods used to construct Calabi-Yau varieties may be extended to complete intersections in non-Fano varieties encoded by star triangulating non-convex polytopes. Similarly, mirror symmetry is conjectured to hold in terms of a transpolar duality generalizing the original construction of Batyrev and Borisov. The associated mirror pairs naturally include certain flip-folded, multi-layered multihedral objects, inclusively named VEX multitopes, and a correspondingly generalized transpolar duality. These self-overlaying VEX multitopes, long since known in pre-symplectic geometry, are found to correspond to certain non-algebraic but smooth toric spaces with Chern classes that satisfy the standard Todd-Hirzebruch identities. The computation of diffeomorphism invariants, including characteristic submanifold intersection numbers, corroborates their recent inclusion in the connected web of Calabi-Yau spaces and associated string compactifications: They arise together with the standard (Fano/reflexive polytope) constructions, within deformation families of generalized complete intersections in products of projective spaces. |
| title | Chern Characteristics and Todd-Hirzebruch Identities for Transpolar Pairs of Toric Spaces |
| topic | High Energy Physics - Theory Algebraic Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2403.07139 |