Refined tropical invariants and characteristic numbers
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914966343254016 |
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| author | Shustin, Eugenii Sinichkin, Uriel |
| author_facet | Shustin, Eugenii Sinichkin, Uriel |
| contents | We prove that the Göttsche-Schroeter and Schroeter-Shustin refined invariants specialize at $q=1$ to the enumeration of rational, resp. elliptic complex curves on arbitrary toric surfaces matching constraints that consist of points and of points with a contact element. Furthermore, we show that the refined invariant extends to the case of any genus $g\ge2$ and either one contact constraint or points in Mikhalkin position, and it again specializes to the corresponding characteristic number at $q=1$. In the appendix we show the limitations of extending this count to a more general setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08420 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Refined tropical invariants and characteristic numbers Shustin, Eugenii Sinichkin, Uriel Algebraic Geometry 14N10, 14T20 We prove that the Göttsche-Schroeter and Schroeter-Shustin refined invariants specialize at $q=1$ to the enumeration of rational, resp. elliptic complex curves on arbitrary toric surfaces matching constraints that consist of points and of points with a contact element. Furthermore, we show that the refined invariant extends to the case of any genus $g\ge2$ and either one contact constraint or points in Mikhalkin position, and it again specializes to the corresponding characteristic number at $q=1$. In the appendix we show the limitations of extending this count to a more general setting. |
| title | Refined tropical invariants and characteristic numbers |
| topic | Algebraic Geometry 14N10, 14T20 |
| url | https://arxiv.org/abs/2408.08420 |