The Kontsevich constants for the volume of the moduli of curves and topological recursion
Chapman, Kevin M. · Mulase, Motohico · Safnuk, Brad
Algebraic Geometry
Mathematical Physics
Combinatorics
Symplectic Geometry
14N35, 05C30, 53D30, 11P21 (Primary) 81T30 (Secondary)
Original · EN
We give an Eynard-Orantin type topological recursion formula for the canonical Euclidean volume of the combinatorial moduli space of pointed smooth algebraic curves. The recursion comes from the edge removal operation on the space of ribbon graphs. As an application we obtain a new proof of the Kontsevich constants for the ratio of the Euclidean and the symplectic volumes of the moduli space of curves.
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