The local/logarithmic correspondence and the degeneration formula for quasimaps
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909989122080768 |
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| author | Rabano, Alberto Cobos Manolache, Cristina Shafi, Qaasim |
| author_facet | Rabano, Alberto Cobos Manolache, Cristina Shafi, Qaasim |
| contents | We study the relationship between the enumerative geometry of rational curves in local geometries and various versions of maximal contact logarithmic curve counts. Our approach is via quasimap theory, and we show versions of the arXiv:1712.05210 local/logarithmic correspondence for quasimaps, and in particular for normal crossings settings, where the Gromov-Witten theoretic formulation of the correspondence fails. The results suggest a link between different formulations of relative Gromov-Witten theory for simple normal crossings divisors via the mirror map. The main results follow from a rank reduction strategy, together with a new degeneration formula for quasimaps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01381 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The local/logarithmic correspondence and the degeneration formula for quasimaps Rabano, Alberto Cobos Manolache, Cristina Shafi, Qaasim Algebraic Geometry 14N35, 14D06, 14A21 We study the relationship between the enumerative geometry of rational curves in local geometries and various versions of maximal contact logarithmic curve counts. Our approach is via quasimap theory, and we show versions of the arXiv:1712.05210 local/logarithmic correspondence for quasimaps, and in particular for normal crossings settings, where the Gromov-Witten theoretic formulation of the correspondence fails. The results suggest a link between different formulations of relative Gromov-Witten theory for simple normal crossings divisors via the mirror map. The main results follow from a rank reduction strategy, together with a new degeneration formula for quasimaps. |
| title | The local/logarithmic correspondence and the degeneration formula for quasimaps |
| topic | Algebraic Geometry 14N35, 14D06, 14A21 |
| url | https://arxiv.org/abs/2404.01381 |