A new family of weighted double Hurwitz numbers and a new ELSV-type formula with $Ω$-classes
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913135589326848 |
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| author | Alexandrov, Alexander Bychkov, Boris Dunin-Barkowski, Petr Kazarian, Maxim Shadrin, Sergey |
| author_facet | Alexandrov, Alexander Bychkov, Boris Dunin-Barkowski, Petr Kazarian, Maxim Shadrin, Sergey |
| contents | We analyze a new family of weighted double Hurwitz numbers that was introduced as a notable example in the context of the $x-y$ duality for logarithmic topological recursion. We use this family to systematically demonstrate, refine and develop techniques that play a crucial role in the interaction of hypergeometric (Orlov--Scherbin) KP tau functions and intersection theory of moduli spaces of curves. In particular, we discuss the subtleties related to the derivation of the ELSV-type formulas in this context and derive a new, explicit ELSV-type formula in terms of the so-called $Ω$-classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00584 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A new family of weighted double Hurwitz numbers and a new ELSV-type formula with $Ω$-classes Alexandrov, Alexander Bychkov, Boris Dunin-Barkowski, Petr Kazarian, Maxim Shadrin, Sergey Algebraic Geometry High Energy Physics - Theory Mathematical Physics Combinatorics 14H10, 05A15, 14N10, 14C17 We analyze a new family of weighted double Hurwitz numbers that was introduced as a notable example in the context of the $x-y$ duality for logarithmic topological recursion. We use this family to systematically demonstrate, refine and develop techniques that play a crucial role in the interaction of hypergeometric (Orlov--Scherbin) KP tau functions and intersection theory of moduli spaces of curves. In particular, we discuss the subtleties related to the derivation of the ELSV-type formulas in this context and derive a new, explicit ELSV-type formula in terms of the so-called $Ω$-classes. |
| title | A new family of weighted double Hurwitz numbers and a new ELSV-type formula with $Ω$-classes |
| topic | Algebraic Geometry High Energy Physics - Theory Mathematical Physics Combinatorics 14H10, 05A15, 14N10, 14C17 |
| url | https://arxiv.org/abs/2605.00584 |