منابع مشابه
Pruned 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 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...
متن کاملOn double Hurwitz numbers with completed cycles
Abstract. In this paper, we collect a number of facts about double Hurwitz numbers, where the simple branch points are replaced by their more general analogues — completed (r + 1)-cycles. In particular, we give a geometric interpretation of these generalised Hurwitz numbers and derive a cut-and-join operator for completed (r+1)-cycles. We also prove a strong piecewise polynomiality property in ...
متن کاملChamber Structure For Double Hurwitz Numbers
Double Hurwitz numbers count covers of the sphere by genus g curves with assigned ramification profiles over 0 and ∞, and simple ramification over a fixed branch divisor. Goulden, Jackson and Vakil (2005) have shown double Hurwitz numbers are piecewise polynomial in the orders of ramification, and Shadrin, Shapiro and Vainshtein (2008) have determined the chamber structure and wall crossing for...
متن کاملOn double Hurwitz numbers in genus 0
We study double Hurwitz numbers in genus zero counting the number of covers CP → CP with two branching points with a given branching behavior. By the recent result due to Goulden, Jackson and Vakil, these numbers are piecewise polynomials in the multiplicities of the preimages of the branching points. We describe the partition of the parameter space into polynomiality domains, called chambers, ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2017
ISSN: 1077-8926
DOI: 10.37236/5761