Structure of Dubrovin-Zhang free energy functions and universal identities
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915280942268416 |
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| author | Shadrin, Sergey Wang, Zhe |
| author_facet | Shadrin, Sergey Wang, Zhe |
| contents | We prove a structural theorem relating the higher genera free energy functions of the Dubrovin-Zhang hierarchies to the Witten-Kontsevich free energy function of the Korteweg-de Vries hierarchy. As an important application, for any given genus $g\geq 1$, we construct a set of universal identities valid for the free energy functions of any Dubrovin-Zhang hierarchy. In particular, we present some techniques that can be used to derive universal identities without relying on the geometry of the moduli space of stable curves of higher genus. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_00276 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Structure of Dubrovin-Zhang free energy functions and universal identities Shadrin, Sergey Wang, Zhe Mathematical Physics Algebraic Geometry We prove a structural theorem relating the higher genera free energy functions of the Dubrovin-Zhang hierarchies to the Witten-Kontsevich free energy function of the Korteweg-de Vries hierarchy. As an important application, for any given genus $g\geq 1$, we construct a set of universal identities valid for the free energy functions of any Dubrovin-Zhang hierarchy. In particular, we present some techniques that can be used to derive universal identities without relying on the geometry of the moduli space of stable curves of higher genus. |
| title | Structure of Dubrovin-Zhang free energy functions and universal identities |
| topic | Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2405.00276 |