{{\mathbb{F}}}_q^\times$. Our main result is that the scheme $B_V$ represents the functor that associates an ${{\mathbb{F}}}_q$-scheme $S$ to the set of isomorphism classes of $V$-ferns over $S$. Thus $V$-ferns over ${{\mathbb{F}}}_q(t)$-schemes can be regarded as generalizations of Drinfeld ${{\mathbb{F}}}_q[t]$-modules with level $(t)$ structure and rank $n$.

To prove this theorem, we construct an explicit universal $V$-fern over $B_V$. We then show that any $V$-fern over a scheme $S$ determines a unique morphism $S\to B_V$, depending only its isomorphism class, and that the $V$-fern is isomorphic to the pullback of the universal $V$-fern along this morphism.

We also give several functorial constructions involving $V$-ferns, some of which are used to prove the main result. These constructions correspond to morphisms between various modular compactifications of Drinfeld period domains over ${{\mathbb{F}}}_q$. We describe these morphisms explicitly.

Zusammenfassung {#zusammenfassung .unnumbered}
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Seien ${{\mathbb{F}}}_q$ ein endlicher Körper mit $q$ Elementen und $V$ ein Vektorraum über ${{\mathbb{F}}}_q$ endlicher Dimension $n>0$. Sei $\OV$ der Drinfeld’sche Periodenbereich über ${{\mathbb{F}}}_q$. Dieser ist ein affines Schema von endlichem Typ über ${{\mathbb{F}}}_q$, dessen Basis-Wechsel nach ${{\mathbb{F}}}_q(t)$ der Modulraum von Drinfeld ${{\mathbb{F}}}_q[t]$-Moduln vom Rang $n$ mit Niveau $(t)$ Struktur ist. In dieser Arbeit geben wir Pinks und Schieders glatter Kompaktifizierung $B_V$ von 