V'\subset V}P_{V'},$ where $V'$ runs over all non-zero subspaces of $V$. It is shown that $B_V$ possesses a natural stratification indexed by the flags of subspaces of $V$ and that the complement $B_V\setminus\OV$ is a divisor with normal crossings. Further properties of $B_V$ are established by Linden [@Lind]. For further details, see Section \[OVBV\].

Smooth $V$-ferns
----------------

We now turn to $V$-ferns, whose definition we motivate in the following paragraphs. Keeping in mind the ever-fruitful analogy between Drinfeld modules and elliptic curves, these $V$-ferns should correspond to generalizations of Drinfeld modules in the spirit of the generalized elliptic curves of Deligne-Rapoport [@Del-Rap]. Indeed, the latter are used to accomplish a task analogous to what one hopes to accomplish for Drinfeld modular varieties, namely, to construct smooth algebraic compactifications of moduli of elliptic curves with given level. On the other hand, we rely heavily on the work of Knudsen [@Knud] concerning the moduli space of stable $n$-pointed curves of a given genus. We recall the definition (with a formulation that is more suited to our purposes) in the case of genus 0:

Let $K$ be a field, and let $I$ be a finite set. A *stable $I$-marked curve of genus $0$* 