The KSBA compactification of a 4-dimensional family of polarized enriques surfaces
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We describe the moduli compactification by stable pairs (also known as KSBA compactification) of a $4$-dimensional family of Enriques surfaces, which arise as specific bidouble covers of the blow up of the projective plane at three general points branched along a configuration of three pairs of lines. The chosen divisor is an appropriate multiple of the ramification locus. We study the degenerations parametrized by the boundary and its stratification. We relate this compactification to the Baily-Borel compactification of the same family of Enriques surfaces. Part of the boundary of this stable pairs compactification has a toroidal behavior, another part is isomorphic to the Baily-Borel compactification, and what remains is a mixture of these two. To conclude, we construct an explicit Looijenga's semitoric compactification whose boundary strata are in bijection with the boundary strata of the KSBA compactification considered.