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arXiv · 0804.0579

Tropical Hurwitz Numbers

Renzo Cavalieri·Paul Johnson·Hannah Markwig
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Abstract

Hurwitz numbers count genus g, degree d covers of the projective line 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.

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Renzo Cavalieri, Paul Johnson, Hannah Markwig. 2010-07-16. Tropical Hurwitz Numbers. https://arxiv.org/abs/0804.0579

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