Completed Cycles Leaky Hurwitz Numbers

2025/02/02 by Accadia, Davide, Karev, Maksim, Lewański, Danilo
#14N35 (Primary) 14T99 (Secondary) #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.00860

Abstract

We introduce (r+1)-completed cycles k-leaky Hurwitz numbers and prove piecewise polynomiality as well as establishing their chamber polynomiality structure and their wall crossing formulae. For k=0 the results recover previous results of Shadrin-Spitz-Zvonkine. The specialization for r=1 recovers Hurwitz numbers that are close to the ones studied by Cavalieri-Markwig-Ranganathan and Cavalieri-Markwig-Schmitt. The ramifications differ by a lower order torus correction, natural from the Fock space perspective, not affecting the genus zero enumeration, nor the enumeration for leaky parameter values k = ± 1 in all genera.

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