More specifically, we are interested in compactifications of such moduli spaces and will focus on the special case of Drinfeld ${{\mathbb{F}}}_q[t]$-modules of generic characteristic and rank $n$ with level $(t)$ structure. In this case, the corresponding fine moduli space is obtained via base change from a *Drinfeld period domain over a finite field* $\OV$, which is an affine algebraic variety over ${{\mathbb{F}}}_q$ (see below for more details). In [@P-Sch], Pink and Schieder construct two projective compactifications of $\OV$ and give each a modular interpretation: the normal *Satake compactification* $Q_V$, and a smooth compactification $B_V$ which dominates $Q_V$. The aim of this thesis is to give $B_V$ a new modular interpretation in terms of geometric objects that we call $V$-ferns. This will hopefully aid in future efforts to construct useful compactifications of more general Drinfeld modular varieties.

Drinfeld Modular Varieties
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Let $C$ be a smooth projective geometrically irreducible curve over ${{\mathbb{F}}}_q$. Let $\infty\in C$ be a closed point and let $A:={{\cal O}}_C(C\setminus\{\infty\}) $. Such an $A$ is called an *admissible coefficient ring*. Let $F:=\Quot(A)$ and let $K$ be a field extension of $F$. The *ring of additive polynomials* $K[\tau]$ is the ring of polynomials in $\tau$ over $K$ subject to 