flag of $V$. We define the notion of an ${{\cal F}}$-fern. For a scheme $S$ and $V$-fern $C$ over $S$, we also define the locus $S_{{\cal F}}\subset S$ over which $C$ is an ${{\cal F}}$-fern. We show that $S_{{\cal F}}$ is open and that the $S_{{\cal F}}$ cover $S$ as ${{\cal F}}$ varies.

**Section 6.**We construct the universal family ${{\cal C}}_V$ over $B_V$. This constitutes the technical bulk of the thesis.

**Section 7.** Here we prove the Main Theorem.

**Section 8.** We consider the morphisms corresponding the each of the constructions described in Section 4 between various moduli schemes.

Notation and conventions {#notation-and-conventions .unnumbered}
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We gather some notation and conventions here for easy reference: $$\begin{aligned}
 {{\mathbb{F}}}_q& &\mbox{ a finite field of $q$ elements};\\
V&&\mbox{ a finite dimensional vector space over ${{\mathbb{F}}}_q$ of dimension $n>0$};\\
\hat V&&\mbox{ the set $V\cup \{\infty\}$ for a new symbol $\infty$.}\\
\mrV&&\mbox{ the set $V\setminus \{0\}$.}\\
G&&\mbox{ the finite group $V\rtimes{{\mathbb{F}}}_q^\times$};\\
S_V&&\mbox{ the symmetric algebra of $V$ over ${{\mathbb{F}}}_q,$}\\
RS_V&&\mbox{ the localization of $S_V$ obtained by inverting all $v\in V\setminus\{0\}$.}\\
P_V&&\mbox{ the scheme }\Proj(S_V);\\
\OV&&\mbox{ the complement of the union of all ${{\mathbb{F}}}_q$-hyperplanes in $P_V$}\\
\Sigma&&\mbox{ the set $V\times\mrV$}\\
P^\Sigma&&\mbox{ the scheme $\prod_{(v,w)\in\Sigma}{{\mathbb{P}}}^1$}.\end{aligned}$$ For a 