منابع مشابه
Tropical Hurwitz numbers
Hurwitz numbers count genus g, degree d covers of P1 with fixed branch locus. This equals the degree of a natural branch map defined on the Hurwitz space. In tropical geometry, algebraic curves are replaced by certain piece-wise linear objects called tropical curves. This paper develops a tropical counterpart of the branch map and shows that its degree recovers classical Hurwitz numbers. Furthe...
متن کاملPruned Double Hurwitz Numbers
Hurwitz numbers count ramified genus g, degree d coverings of the projective line with fixed branch locus and fixed ramification data. Double Hurwitz numbers count such covers, where we fix two special profiles over 0 and ∞ and only simple ramification else. These objects feature interesting structural behaviour and connections to geometry. In this paper, we introduce the notion of pruned doubl...
متن کاملLozenge Tilings and Hurwitz Numbers
We give a new proof of the fact that, near a turning point of the frozen boundary, the vertical tiles in a uniformly random lozenge tiling of a large sawtooth domain are distributed like the eigenvalues of a GUE random matrix. Our argument uses none of the standard tools of integrable probability. In their place, it uses a combinatorial interpretation of the HarishChandra/Itzykson-Zuber integra...
متن کاملGenerating Functions for Hurwitz-Hodge Integrals
In this paper we describe explicit generating functions for a large class of Hurwitz-Hodge integrals. These are integrals of tautological classes on moduli spaces of admissible covers, a (stackily) smooth compactification of the Hurwitz schemes. Admissible covers and their tautological classes are interesting mathematical objects on their own, but recently they have proved to be a useful tool f...
متن کاملTowards the Geometry of Double Hurwitz Numbers
Double Hurwitz numbers count branched covers of CP with fixed branch points, with simple branching required over all but two points 0 and∞, and the branching over 0 and∞ points specified by partitions of the degree (withm and n parts respectively). Single Hurwitz numbers (or more usually, Hurwitz numbers) have a rich structure, explored by many authors in fields as diverse as algebraic geometry...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2020
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.5130554