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We derive the partition function of N=4 supersymmetric Yang-Mills theory on orbifold-. In classical geometry, K3 surface is constructed from the orbifold-. Along the same way as the orbifold construction, we construct the partition function of K3 surface from orbifold-$T^4/{\bf Z}_2$. The partition function is given by the product of the contribution of the untwisted sector of , and that of the twisted sector of i.e., curve blow-up formula.

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