$k$-leaky double Hurwitz descendants

Renzo Cavalieri; Hannah Markwig; Johannes Schmitt

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arXiv · 2404.10168

$k$-leaky double Hurwitz descendants

Renzo Cavalieri·Hannah Markwig·Johannes Schmitt

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Abstract

We define a new class of enumerative invariants called $k$-leaky double Hurwitz descendants, generalizing both descendant integrals of double ramification cycles and the $k$-leaky double Hurwitz numbers introduced in previous work of Cavalieri, Markwig and Ranganathan. These numbers are defined as intersection numbers of the logarithmic DR cycle against $\psi$-classes and logarithmic classes coming from piecewise polynomials encoding fixed branch point conditions. We give a tropical graph sum formula for these new invariants, allowing us to show their piecewise polynomiality and a wall-crossing formula in genus zero. We also prove that in genus zero the invariants are always non-negative and give a complete classification of the cases where they vanish.

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Renzo Cavalieri, Hannah Markwig, Johannes Schmitt. 2024-04-15. $k$-leaky double Hurwitz descendants. https://arxiv.org/abs/2404.10168

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