Very minor fixes

scv.tex

@@ -15681,8 +15681,8 @@ \section{Hypervarieties} \label{section:hypervarieties}
 More precisely,
 suppose $X$ is a pure codimension-$1$ subvariety
 of a small enough
-neighborhood
-$U' \times D \subset \C^{n-1} \times \C$ of the origin, where $D$ is a disc,
+polydisc
+$U' \times D \subset \C^{n-1} \times \C$ centered at the origin,
 and the function that vanishes on $X$ is a
 Weierstrass polynomial $P(z',z_n)$ defined for $z' \in U'$, and
 all zeros of $z_n \mapsto P(z',z_n)$ are in $D$ for $z' \in U$.
@@ -16370,9 +16370,10 @@ \section{Irreducibility, local parametrization, and Puiseux}
 And for larger-dimensional varieties, we can find
 enough one-dimensional curves through any point and parametrize those.
 
-It is not true that every subvariety is an injective image of a piece of
+It is not true that every irreducible subvariety is locally
+an injective image of a piece of
 $\C^k$ via a holomorphic map, but it is a very deep theorem,
-the resolution of singularities, that you can do so if you allow some points
+the resolution of singularities, that says you can do so if you allow some points
 where the function is not one-to-one.
 
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