NDLI: Tropical Hurwitz numbers

Content Provider	Springer Nature Link
Author	Cavalieri, Renzo Johnson, Paul Markwig, Hannah
Copyright Year	2009
Abstract	Hurwitz numbers count genus g, degree d covers of ℙ$^{1}$ 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. Further, the combinatorial techniques developed are applied to recover results of Goulden et al. (in Adv. Math. 198:43–92, 2005) and Shadrin et al. (in Adv. Math. 217(1):79–96, 2008) on the piecewise polynomial structure of double Hurwitz numbers in genus 0.
Starting Page	241
Ending Page	265
Page Count	25
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	32
Issue Number	2
e-ISSN	15729192
Language	English
Publisher	Springer US
Publisher Date	2009-12-24
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Group Theory and Generalizations Computer Science Order, Lattices, Ordered Algebraic Structures Convex and Discrete Geometry Combinatorics
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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Tropical Hurwitz numbers