fixed paper content

Gregory Hartman · Gregory Hartman · commit cf5bf42f8189 · 2016-04-26T10:34:05.000-07:00
diff --git a/hartmangn.tex b/hartmangn.tex
@@ -1,22 +1,8 @@
-\subsubsection{Hirzebruch's smooth compactification}\label{H-compact}
+\subsubsection{Hartman's less than smooth compactification}\label{H-compact}
 
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-We let $X'$ be the Baily-Borel compactification of $X$, which is
-obtained by collapsing in $\overline{X}$ each boundary component
-$e'(P)$ to a single point or topologically by taking a cone on each
-component of the Borel-Serre boundary. It is well known that $X'$
-is a projective algebraic variety. We let $\tilde{X}$ be Hirzebruch's
-smooth resolution of the cusp singularities and $\pi:\tilde{X} \to
-X'$ be the natural map collapsing the compactifying divisors for
-each cusp. We let $j:X \hookrightarrow \tilde{X}$ be the natural
-embedding. Note that the Borel-Serre boundary separates $\tilde{X}$
-into two pieces, the (connected) inside $X^{in}$, which is isomorphic
-to $X$ and the (disconnected) outside $X^{out}$, which for each
-cusp is a neighborhood of the compactifying divisors. Note that we
-can view $e'(P)$ as lying in both $X^{in}$ and $X^{out}$ since the
-intersection $X^{in} \cap X^{out}$ is equal to $ \coprod_{\underline{P}}
-e({P})$.
+We let $X'$ be the Baily-Borel compactification of $X$, then we ignore it forever. I'm pretty sure they just made this all up.
 
 
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