Refine statement of theorem: bound on r #3

main.tex

@@ -1188,10 +1188,11 @@ which also guarantees that the gap $\frac{k}{2mn^2}$ is at least $\epsilon_{q,2}
 
 \begin{theorem}[Bound on $r$ \#3]
 \label{thm:rmax_with_eps1}
-	Let $v = (R,C,D)$ be a fixed Chern character. Then the ranks of the
-	pseudo-semistabilizers for $v$ with
-	$\chern_1^\beta = q = \frac{a_q}{n}$
-	are bounded above by the following expression (with $i=1$ or 2).
+	Let $v$ be a fixed Chern character, with $\frac{a_F}{n}=\beta:=\beta(v)$
+	rational and expressed in lowest terms.
+	Then the ranks $r$ of the pseudo-semistabilizers $u$ for $v$ with
+	$\chern_1^\beta(u) = q = \frac{b_q}{n}$
+	are bounded above by the following expression (with $i=1$ or $2$).
 
 \begin{sagesilent}
 eps_k_i_subs = Delta == (2*m*n^2)/delta
@@ -1208,7 +1209,11 @@ eps_k_i_subs = Delta == (2*m*n^2)/delta
 		\right)
 	\end{align*}
 	\egroup
-	Where $\epsilon_{q,i}$ is defined as in definition/lemma \ref{lemdfn:epsilon_q}.
+	Where $k_{q,i}$ is defined as in definition/lemma \ref{lemdfn:epsilon_q},
+	and $R = \chern_0(v)$
+
+	Furthermore, if $\aa \not= 0$ then
+	$r \equiv \aa^{-1}b_q (\mod n)$.
 \end{theorem}