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A surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero. This is analogous to a curve generalizing a straight line

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'Reference' request: Program to work with cyclic quotient singularities.

On page 19 of http://www.cems.uvm.edu/~voight/notes/cfrac.pdf is a maple program for computing the so-called Hirzebruch-Jung continued fraction expansion. So that's (1). For (2), at least when $n$ is …
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