From d29a4adb2283a18a6bbe06eb6ad38c8538f535a7 Mon Sep 17 00:00:00 2001
From: jgarnek <jgarnek@amu.edu.pl>
Date: Wed, 18 Dec 2024 12:54:34 +0100
Subject: [PATCH] X ---> X/C cases

---
 article_de_rham_cyclic.tex | 11 ++++++++++-
 1 file changed, 10 insertions(+), 1 deletion(-)

diff --git a/article_de_rham_cyclic.tex b/article_de_rham_cyclic.tex
index 28295c5..e999175 100644
--- a/article_de_rham_cyclic.tex
+++ b/article_de_rham_cyclic.tex
@@ -924,7 +924,7 @@ Indeed, ????. The ramification points of $\pi : X \to X/G$ are as follows:
 	\item[] (their stabilizers are subgroups $C_1 = C$, $\ldots$, $C_p$
 	conjugated to $C$),
 	
-	\item point $P_{\infty}$ above $Q_{\infty}$ (its stabilizer is $G$),
+	\item a point $P_{\infty}$ above $Q_{\infty}$ (its stabilizer is $G$),
 	
 	\item points $P_i^{(1)}, \ldots, P_i^{(p \cdot (p-1))}$ above $Q_i$ for $i = 1, \ldots, N$
 	\item[] (their stabilizers equal $C'$).
@@ -933,6 +933,15 @@ Indeed, ????. The ramification points of $\pi : X \to X/G$ are as follows:
 The same points are in the ramification locus of the morphism $X \to X/C$ with the following
 ramification groups:
 %
+\[
+	C_{P_i^{(j)}} =
+	\begin{cases*}
+		C, & \textrm{ if } (i, j) = \\
+		C', &
+	\end{cases*}
+\]
+
+
 \begin{align*}
 	C_{P_0^{(1)}} &= C\\
 	C_{P_0^{(i)}} &= C' \qquad \textrm{ for } i > 1,\\