Although K3 surfaces and Enriques surfaces are closely related, their moduli spaces behave very differently. As the degree increases, one one obtains an infinite series of different moduli spaces of polarized K3 surfaces., In contrast, there are only finitely many different moduli spaces of (numerically) polarized Enriques surfaces. In fact there are exactly 87 orthogonal modular varieties which appear in context with moduli of polarized Enriques surfaces. Together with Dutour-Sikiric we classified the corresponding arithmetic groups. I will discuss this classification and related questions.
Moduli of polarized Enriques surfaces Sponsored by the Meyer Fund
Moduli of polarized Enriques surfaces