Spin refinement of moduli spaces of residueless meromorphic differentials and the BKP hierarchy
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912411131314176 |
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| author | Klompenhouwer, David Velstra, Stijn |
| author_facet | Klompenhouwer, David Velstra, Stijn |
| contents | We consider strata of curves carrying a residueless meromorphic differential inducing a spin structure on the curve. The cohomology classes of the closures of these strata, weighted by the parity of the spin structures, form a partial cohomological field theory (CohFT) of infinite rank. After applying the DR hierarchy construction to this partial CohFT and reducing to differentials with two zeros and arbitrarily many poles, we show that the resulting system of evolutionary PDEs coincides with the BKP hierarchy up to a coordinate transformation. This is a spin refinement of an analogous result from arXiv:2110.01419. Our proof relies on a new result regarding the reconstruction of the BKP hierarchy from a limited amount of information in the Lax formalism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02540 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spin refinement of moduli spaces of residueless meromorphic differentials and the BKP hierarchy Klompenhouwer, David Velstra, Stijn Algebraic Geometry Mathematical Physics Exactly Solvable and Integrable Systems 14H81, 37K10 We consider strata of curves carrying a residueless meromorphic differential inducing a spin structure on the curve. The cohomology classes of the closures of these strata, weighted by the parity of the spin structures, form a partial cohomological field theory (CohFT) of infinite rank. After applying the DR hierarchy construction to this partial CohFT and reducing to differentials with two zeros and arbitrarily many poles, we show that the resulting system of evolutionary PDEs coincides with the BKP hierarchy up to a coordinate transformation. This is a spin refinement of an analogous result from arXiv:2110.01419. Our proof relies on a new result regarding the reconstruction of the BKP hierarchy from a limited amount of information in the Lax formalism. |
| title | Spin refinement of moduli spaces of residueless meromorphic differentials and the BKP hierarchy |
| topic | Algebraic Geometry Mathematical Physics Exactly Solvable and Integrable Systems 14H81, 37K10 |
| url | https://arxiv.org/abs/2506.02540 |