diff --git a/generaldegreeHypersurfaces.tex b/generaldegreeHypersurfaces.tex
index fb7dd20..adbc137 100644
--- a/generaldegreeHypersurfaces.tex
+++ b/generaldegreeHypersurfaces.tex
@@ -83,10 +83,10 @@ Therefore, we will work with $C_d$, from now on.
 
 We will denote:
 \begin{eqnarray*}
-	M_d&=&\{(x_0,\dots,x_n)\in\CC^{n+1} | \sum x^d_i=1\} \\
-	S_d&=&\{(x_0,\dots,x_n)\in M_d | x^d_i\in\RR_{\geq0} \forall i\} \\
+	M_d&=&\left\{(x_0,\dots,x_n)\in\CC^{n+1}\, \middle|\, \sum x^d_i=1\right\} \\
+	S_d&=&\left\{(x_0,\dots,x_n)\in M_d\,\middle|\, x^d_i\in\RR_{\geq0} \forall i\right\} \\
 	K &=&\pi(S_d)
-%)\{[x_0:\dots:x_{n}]\in\CC\PP^n \setminus M_2 | x^d_i\in\RR_{\geq0} \forall i\}
+%\{[x_0:\dots:x_{n}]\in\CC\PP^n \setminus M_2 | x^d_i\in\RR_{\geq0} \forall i\}
 \end{eqnarray*}
 where $\proy{}:\CC^{n+1}\setminus\{\mathbf{0}\}\to\PP^n$ is the quotient map.
 We then have a commutative diagram:
@@ -463,7 +463,7 @@ We denote as $\Delta$ the $\Delta-$complex $[v_0, \dots, v_n]$ that has $n+1$ ve
 \begin{tikzcd}
 \Delta \rar[leftrightarrow]& S_1&\\ 
 \Delta^d\uar\rar[leftrightarrow]&S_d\uar\rar[hookrightarrow]\dar& M_d\dar\\ 
-&K \rar[hookrightarrow]& \PP^2\setminus C_d,
+&K \rar[hookrightarrow]& \PP^n\setminus C_d,
 \end{tikzcd}
 \end{equation*}
 where $\Delta^d$ is a $\Delta-$complex that we are trying to find and identify with $S_d$, equivalently as what we have done for $d=1$. Since $S_d$ is a ramified cover of $S_1$ by the power to the $d$ map, we want $\Delta^d$ to be a ramified cover of $\Delta$ by the same map.