Birational Invariance in Punctured Log Gromov-Witten Theory
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917881586909184 |
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| author | Johnston, Samuel |
| author_facet | Johnston, Samuel |
| contents | Given a log smooth scheme $(X,D)$, and a log étale modification $(\tilde{X},\tilde{D}) \rightarrow (X,D)$, we relate the punctured Gromov-Witten theory of $(\tilde{X},\tilde{D})$ to the punctured Gromov-Witten theory of $(X,D)$, generalizing results of Abramovich and Wise in the non-punctured setting in "Birational invariance in log Gromov-Witten Theory". Using the main comparison results, we show a form of log étale invariance for the logarithmic mirror algebras and canonical scattering diagrams constructed in "Intrinsic Mirror Symmetry" and "The Canonical Wall Structure and Intrinsic Mirror Symmetry" respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_06079 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Birational Invariance in Punctured Log Gromov-Witten Theory Johnston, Samuel Algebraic Geometry Given a log smooth scheme $(X,D)$, and a log étale modification $(\tilde{X},\tilde{D}) \rightarrow (X,D)$, we relate the punctured Gromov-Witten theory of $(\tilde{X},\tilde{D})$ to the punctured Gromov-Witten theory of $(X,D)$, generalizing results of Abramovich and Wise in the non-punctured setting in "Birational invariance in log Gromov-Witten Theory". Using the main comparison results, we show a form of log étale invariance for the logarithmic mirror algebras and canonical scattering diagrams constructed in "Intrinsic Mirror Symmetry" and "The Canonical Wall Structure and Intrinsic Mirror Symmetry" respectively. |
| title | Birational Invariance in Punctured Log Gromov-Witten Theory |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2210.06079 |