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math.GT2015
On balanced planar graphs, following W. Thurston
Sarah Koch, Tan Lei
Let be an orientation-preserving branched covering map of degree , and let be an oriented Jordan curve passing through the critical values of . Then…
math.GT2013
An analytic construction of the Deligne-Mumford compactification of the moduli space of curves
John H. Hubbard, Sarah Koch
In 1969, P. Deligne and D. Mumford compactified the moduli space of curves. Their compactification is a projective algebraic variety, and as such, it has an underlying analytic str…