Intrinsic Mirror Symmetry
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866908567285530624 |
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| author | Gross, Mark Siebert, Bernd |
| author_facet | Gross, Mark Siebert, Bernd |
| contents | We associate a ring R to a log Calabi-Yau pair (X,D) or a degeneration of Calabi-Yau manifolds X->B. The vector space underlying R is determined by the tropicalization of (X,D) or X->B, while the product rule is defined using punctured Gromov-Witten invariants, defined in joint work with Abramovich and Chen. In the log Calabi-Yau case, if D is maximally degenerate, then we propose that Spec R is the mirror to X\D, while in the Calabi-Yau degeneration case, if the degeneration is maximally unipotent, the mirror is expected to be Proj R. The main result in this paper is that R as defined is an associative, commutative ring with unit, with associativity the most difficult part. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_07649 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Intrinsic Mirror Symmetry Gross, Mark Siebert, Bernd Algebraic Geometry 14J33 We associate a ring R to a log Calabi-Yau pair (X,D) or a degeneration of Calabi-Yau manifolds X->B. The vector space underlying R is determined by the tropicalization of (X,D) or X->B, while the product rule is defined using punctured Gromov-Witten invariants, defined in joint work with Abramovich and Chen. In the log Calabi-Yau case, if D is maximally degenerate, then we propose that Spec R is the mirror to X\D, while in the Calabi-Yau degeneration case, if the degeneration is maximally unipotent, the mirror is expected to be Proj R. The main result in this paper is that R as defined is an associative, commutative ring with unit, with associativity the most difficult part. |
| title | Intrinsic Mirror Symmetry |
| topic | Algebraic Geometry 14J33 |
| url | https://arxiv.org/abs/1909.07649 |