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arXiv · 2509.04335

One part leaky covers

Renzo Cavalieri·Hannah Markwig·Johannes Schmitt
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Abstract

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.

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Renzo Cavalieri, Hannah Markwig, Johannes Schmitt. 2025-09-04. One part leaky covers. https://arxiv.org/abs/2509.04335

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