Let me start with an apologetic disclaimer: I am very far from an algebraic geometer, so this question might be crudely formulated.

I have a specific question about du Val singularities, but while trying to dig up information about it online I've ended up with a more general question as well. In everything below, I am assuming that I'm working over $\mathbb{C}$.

**General question**

A smooth variety/(reduced, separated, of finite type, etc.) scheme comes with an atlas of open affines. The variety is called *uniformly rational* if it admits an atlas of open affines each of which is itself a Zariski open subset of affine space $\mathbb{A}^d$.

An even stronger condition that one might ask for is an atlas where each open affine is in fact a copy of $\mathbb{A}^d$ itself. In other words, the variety should be locally isomorphic to affine space. Obvious examples are projective space itself and total spaces of line bundles over projective space, for example.

My general question is whether this class of varieties has a name, or is known to be so restrictive as to be totally uninteresting (I realize that already the requirement that the variety be rational is already quite restrictive).

**Specific question**

A slightly more interesting class of examples that can be seen to be locally affine in the above sense are the minimal resolutions of $A$-type du Val singularities. Blowing up the singularity provides exactly such an atlas of $\mathbb{A}^2$ patches.

It appears to me that the same is true of (minimal resolutions of) the $D$-type (and possibly $E$-type) singularities as well, though this is not provided for you automatically by doing a textbook blow-up to realize the minimal resolutions.

My specific question is whether such an atlas for resolutions of du Val singularities is a standard thing, or if this claim is somehow obvious (or, alternatively, if the claim is obviously false indicating an error on my part).