Cell decompositions of moduli space, lattice points and Hurwitz problems
نویسنده
چکیده
In this article we describe the cell decompositions of the moduli space of Riemann surfaces due to Harer, Mumford and Penner and its relationship to a Hurwitz problem. The cells possess natural linear structures and with respect to this they can be described as rational convex polytopes. We show how to effectively calculate the number of lattice points and the volumes over all cells. These calculations contain deep information about the moduli space.
منابع مشابه
Hurwitz spaces
1.1 The classical Hurwitz space and the moduli of curves The classical Hurwitz space first appeared in the work of Clebsch [5] and Hurwitz [17] as an auxiliary object to study the moduli space of curves. Let X be a smooth projective curve of genus g over C. A rational function f : X → P of degree n is called simple if there are at least n − 1 points on X over every point of P. Such a cover has ...
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