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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.04335 |
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| _version_ | 1866912570322976768 |
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| author | Cavalieri, Renzo Markwig, Hannah Schmitt, Johannes |
| author_facet | Cavalieri, Renzo Markwig, Hannah Schmitt, Johannes |
| contents | In our previous work [CMS24] we defined a new class of enumerative invariants called $k$-leaky double Hurwitz descendants, generalizing both descendant integrals of double ramification cycles and $k$-leaky double Hurwitz numbers. Here, we focus on the one-part version of these numbers, i.e.\ when the positive ramification profile is $(d)$. We derive recursions and use them to produce explicit formulas and structure results for some infinite families of these numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04335 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One part leaky covers Cavalieri, Renzo Markwig, Hannah Schmitt, Johannes Algebraic Geometry Combinatorics In our previous work [CMS24] we defined a new class of enumerative invariants called $k$-leaky double Hurwitz descendants, generalizing both descendant integrals of double ramification cycles and $k$-leaky double Hurwitz numbers. Here, we focus on the one-part version of these numbers, i.e.\ when the positive ramification profile is $(d)$. We derive recursions and use them to produce explicit formulas and structure results for some infinite families of these numbers. |
| title | One part leaky covers |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2509.04335 |