Tropical Hurwitz numbers
نویسندگان
چکیده
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. 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.
منابع مشابه
ar X iv : 0 80 6 . 08 36 v 1 [ m at h . A G ] 4 J un 2 00 8 p - ADIC HURWITZ NUMBERS
We introduce stable tropical curves, and use these to count covers of the p-adic projective line of fixed degree and ramification types by Mumford curves in terms of tropical Hurwitz numbers. Our counts depend on the branch loci of the covers.
متن کاملar X iv : 0 80 6 . 08 36 v 2 [ m at h . A G ] 4 J un 2 00 8 p - ADIC HURWITZ NUMBERS
We introduce stable tropical curves, and use these to count covers of the p-adic projective line of fixed degree and ramification types by Mumford curves in terms of tropical Hurwitz numbers. Our counts depend on the branch loci of the covers.
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