Homological mirror symmetry for complete intersections in algebraic tori
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916250690519040 |
|---|---|
| author | Morimura, Hayato Sibilla, Nicolò Zhou, Peng |
| author_facet | Morimura, Hayato Sibilla, Nicolò Zhou, Peng |
| contents | We prove one direction of homological mirror symmetry for complete intersections in algebraic tori, in all dimensions. The mirror geometry is not a space but a LG model, i.e. a pair given by a space and a regular function. We show that the Fukaya category of the complete intersection is equivalent to the category of matrix factorizations of the LG pair. Our approach yields new results also in the hypersurface setting, which was treated earlier by Gammage and Shende. Our argument depends on breaking down the complete intersection into smaller more manageable pieces, i.e. finite covers of products of higher dimensional pairs-of-pants, thus implementing a program first suggested by Seidel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_06955 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Homological mirror symmetry for complete intersections in algebraic tori Morimura, Hayato Sibilla, Nicolò Zhou, Peng Symplectic Geometry Algebraic Geometry We prove one direction of homological mirror symmetry for complete intersections in algebraic tori, in all dimensions. The mirror geometry is not a space but a LG model, i.e. a pair given by a space and a regular function. We show that the Fukaya category of the complete intersection is equivalent to the category of matrix factorizations of the LG pair. Our approach yields new results also in the hypersurface setting, which was treated earlier by Gammage and Shende. Our argument depends on breaking down the complete intersection into smaller more manageable pieces, i.e. finite covers of products of higher dimensional pairs-of-pants, thus implementing a program first suggested by Seidel. |
| title | Homological mirror symmetry for complete intersections in algebraic tori |
| topic | Symplectic Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2303.06955 |