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 کاملCombinatorics of Tropical Hurwitz Cycles
We study properties of the tropical double Hurwitz loci defined by Bertram, Cavalieri and Markwig. We show that all such loci are connected in codimension one. If we mark preimages of simple ramification points, then for a generic choice of such points the resulting cycles are weakly irreducible, i.e. an integer multiple of an irreducible cycle. We study how Hurwitz cycles can be written as div...
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: Rendiconti del Seminario Matematico della Università di Padova
سال: 2011
ISSN: 0041-8994
DOI: 10.4171/rsmup/125-10