Topological recursion on transalgebraic spectral curves and Atlantes Hurwitz numbers
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909761277001728 |
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| author | Bouchard, Vincent Kramer, Reinier Weller, Quinten |
| author_facet | Bouchard, Vincent Kramer, Reinier Weller, Quinten |
| contents | Given a spectral curve with exponential singularities (which we call a "transalgebraic spectral curve"), we extend the definition of topological recursion to include contributions from the exponential singularities in a way that is compatible with limits of sequences of spectral curves. This allows us to prove the topological recursion/quantum curve correspondence for a large class of transalgebraic spectral curves. As an application, we find that Atlantes Hurwitz numbers, which were previously thought to fall outside the scope of topological recursion, satisfy (our extended version of) topological recursion, and we construct the corresponding quantum curve directly from topological recursion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07433 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topological recursion on transalgebraic spectral curves and Atlantes Hurwitz numbers Bouchard, Vincent Kramer, Reinier Weller, Quinten Mathematical Physics Algebraic Geometry Combinatorics 14H70, 14N10, 05A15, 05E05 Given a spectral curve with exponential singularities (which we call a "transalgebraic spectral curve"), we extend the definition of topological recursion to include contributions from the exponential singularities in a way that is compatible with limits of sequences of spectral curves. This allows us to prove the topological recursion/quantum curve correspondence for a large class of transalgebraic spectral curves. As an application, we find that Atlantes Hurwitz numbers, which were previously thought to fall outside the scope of topological recursion, satisfy (our extended version of) topological recursion, and we construct the corresponding quantum curve directly from topological recursion. |
| title | Topological recursion on transalgebraic spectral curves and Atlantes Hurwitz numbers |
| topic | Mathematical Physics Algebraic Geometry Combinatorics 14H70, 14N10, 05A15, 05E05 |
| url | https://arxiv.org/abs/2304.07433 |