Let us work over a ground field of characteristic zero. As is well-known, a K3 surface is a smooth projective geometrically integral surface $X$ whose canonical class $\omega_X$ is trivial and for which $\operatorname{H}^1(X,\mathscr{O}_X)$ vanishes.

A bit of folklore (proven e.g. in Beauville's *Complex Algebraic Surfaces*) is that if $X$ is a *smooth* complete intersection of a quadric and a cubic in $\mathbb{P}^4$, or a smooth complete intersection of three quadrics in $\mathbb{P}^5$, then $X$ is K3.

### The question

Suppose I have a (non-smooth) complete intersection $X_{2,3}$ of a quadric and a cubic in $\mathbb{P}^4$ *all of whose singularities are rational double points*, and a (non-smooth) complete intersection $X_{2,2,2}$ of three quadrics in $\mathbb{P}^5$, again with at most rational double points.

Do these two surfaces have K3 surfaces as their minimal regular models?

I suspect the answer is **yes**; for example, since the singularities are assumed to be rational double points, they should admit a crepant resolution. However, I can't really locate this fact in the literature. As for the vanishing of the appropriate $\operatorname{H}^1$, I really haven't a clue.