Double Hurwitz numbers and multisingularity loci in genus 0

Maxim Kazarian , Sergey Lando , Dimitri Zvonkine (1, 2)

1 IMJ - Institut de Mathématiques de Jussieu
2 LMV - Laboratoire de Mathématiques de Versailles

In the Hurwitz space of rational functions on the complex projective line 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 Poincaré dual cohomology classes of these loci and deduce a differential equation on Hurwitz numbers.

Domaines: Mathématiques [math]; Géométrie algébrique [math.AG]

Maxim Kazarian, Sergey Lando, Dimitri Zvonkine. Double Hurwitz numbers and multisingularity loci in genus 0. International Mathematics Research Notices, 2022, 2022 (12), pp.9529-9570. ⟨10.1093/imrn/rnab010⟩. ⟨hal-02329296⟩