Arctic curves of periodic dimer models and generalized discriminants
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910660989812736 |
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| author | Piorkowski, Mateusz |
| author_facet | Piorkowski, Mateusz |
| contents | We compute the algebraic equation for arctic curves of the Aztec diamond with a doubly (quasi-)periodic weight structure and obtain similar results for certain models of the hexagon. In particular, we determine the algebraic degree of such curves as a function of the number of frozen and smooth (or gaseous) regions. The key to our result is the construction of a discriminant for meromorphic differentials on a higher genus Riemann surface. This construction works analogously for meromorphic sections of arbitrary holomorphic line bundles. In the genus $g = 0$ case this notion reduces to the usual discriminant of a polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17138 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arctic curves of periodic dimer models and generalized discriminants Piorkowski, Mateusz Mathematical Physics Algebraic Geometry Complex Variables Probability 14K25, 14H70, 52C20 We compute the algebraic equation for arctic curves of the Aztec diamond with a doubly (quasi-)periodic weight structure and obtain similar results for certain models of the hexagon. In particular, we determine the algebraic degree of such curves as a function of the number of frozen and smooth (or gaseous) regions. The key to our result is the construction of a discriminant for meromorphic differentials on a higher genus Riemann surface. This construction works analogously for meromorphic sections of arbitrary holomorphic line bundles. In the genus $g = 0$ case this notion reduces to the usual discriminant of a polynomial. |
| title | Arctic curves of periodic dimer models and generalized discriminants |
| topic | Mathematical Physics Algebraic Geometry Complex Variables Probability 14K25, 14H70, 52C20 |
| url | https://arxiv.org/abs/2410.17138 |