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arXiv · 1908.00455

Double Hurwitz numbers and multisingularity loci in genus 0

Maxim Kazarian·Sergei Lando·Dimitri Zvonkine
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Abstract

In the Hurwitz space of rational functions on CP^1 with poles of given orders, we study the loci of multisingularities, that is, the loci of functions with a given ramification profile over 0. We prove a recursion relation on the Poincare dual cohomology classes of these loci and deduce a differential equation on Hurwitz numbers.

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Maxim Kazarian, Sergei Lando, Dimitri Zvonkine. 2019-08-01. Double Hurwitz numbers and multisingularity loci in genus 0. https://arxiv.org/abs/1908.00455

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