On the Torus Degeneration of the Genus Two Partition Function

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We consider the partition function of a general vertex operator algebra V on a genus two Riemann surface formed by sewing together two tori. We consider the non-trivial degeneration limit where one torus is pinched down to a Riemann sphere and show that the genus one partition function on the degenerate torus is recovered up to an explicit universal V-independent multiplicative factor raised to the power of the central charge.