A reference for the density of singular K3 surfaces in the period domain (see Will Sawin's comment) is

<cite authors="Piatetski-Shapiro, Ilya I.; Shafarevich, I. R.">_Piatetski-Shapiro, Ilya I.; Shafarevich, I. R._, Arithmetic of K3 surfaces, Trudy Mezhdunarod. Konf. Teor. Chisel, Moskva 1971, Tr. Mat. Inst. Steklova 132, 44-54 (1973) [ZBL0293.14010](https://zbmath.org/?q=an:0293.14010).</cite>

In particular, this is a screenshot of page 54:

[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/woBjn.png