Type II degenerations of K3 surfaces of degree 4

Moduli spaces of K3 surfaces have long been studied, beginning with the proof of the Torelli theorem for K3s in the 70s. The most well-known compactificaton of this moduli space is still probably the Baily-Borel compactification, whose boundary components consist of Type II and Type III degenerations. Meanwhile, the GIT compactification is able to explicitly describe its boundary components, often by equations as studied by Shah in the 80s and more recently by Laza and O'Grady. In this talk we provide the requisite definitions of degenerations and moduli spaces, giving examples along the way. The goal of the talk is to explicitly demonstrate a correspondence between the Type II boundary components of the Baily-Borel compactification and Type II boundary components of the GIT compactifcation for the moduli space of K3 surfaces of degree 4.