\documentclass{amsart}

%First, compile a pdf with pdflatex.  Next, use pdfcrop (command line).  Finally use pdf2svg to convert to svg

\usepackage{xypic}
\xyoption{all}

\begin{document}
\thispagestyle{empty}
$$
\xymatrix{
\operatorname{GL}(V)\ar[rr]^r&&\operatorname{PGL}(V)\\
\operatorname{SL}(2,\mathbb C)\ar[rr]^p\ar[u]^\Phi&&\operatorname{SO}^+(3,1)\ar[u]^{\Pi^*}\ar@{-->}[llu]^\Pi\\
\mathfrak{sl}(2,\mathbb C)\ar[rr]^\sigma\ar[u]^{\operatorname{exp}}\ar[rd]^\Phi&&\mathfrak{so}(3,1)\ar[u]^{\operatorname{exp}}\ar[ld]^\pi\\
&\operatorname{End}(V)&
}
$$