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Inspired by the ideas of the minimal model program, Shepherd-Barron,Koll\'ar, and Alexeev have constructed a geometric compactification for themoduli space of surfaces of log general type. In this paper, we discuss one ofthe simplest examples that fits into this framework: the case of pairs (X,H)consisting of a degree two K3 surface X and an ample divisor H. Specifically,we construct and describe explicitly a geometric compactification $\bar{P_2}$for the moduli of degree two K3 pairs. This compactification has a naturalforgetful map to the Baily-Borel compactification of the moduli space $F_2$ ofdegree two K3 surfaces. Using this map and the modular meaning of $\bar{P_2}$,we obtain a better understanding of the geometry of the standardcompactifications of $F_2$.

The KSBA compactification for the moduli space of degree two K3 pairs