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We present a twistor-like formula for the complete tree-level S matrix of 6D$(2,0)$ supergravity coupled to $21$ abelian tensor multiplets. This is thelow-energy effective theory that corresponds to Type IIB superstring theorycompactified on a $\mathrm{K}3$ surface. The formula is expressed as anintegral over the moduli space of certain rational maps of the puncturedRiemann sphere. By studying soft limits of the formula, we are able to explorethe local moduli space of this theory, ${SO(5,21)\over SO(5)\times SO(21)}$.Finally, by dimensional reduction, we also obtain a new formula for thetree-level S matrix of 4D $\mathcal{N}=4$ Einstein-Maxwell theory.

All Tree Amplitudes of 6D $(2,0)$ Supergravity: Interacting Tensor Multiplets and the $K3$ Moduli Space