Resolving quotient singularities III

To conclude this miniseries on resolutions of quotient singularities, I present the full toric picture of what is happening, including gory computations of the self-intersections of exceptional curves in terms of Jung-Hirzebruch continued fractions. The intricacy of the computations maybe conceals the conciseness of the toric lexicon: these three pages of computations are best summarised by the following picture for the quotient singularity \frac{1}{7}(1,5)

1over7

From it one can immediately read that its [minimal] resolution has three exceptional curves with discrepancies -1/7, -2/7, and -3/7. From the continued fraction expansion of \frac{7}{5}=[2,2,3] one gains the equivalent information that there are three exceptional curves with self-intersection -2,-2, and -3.

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