\relax 
\citation{GHS}
\citation{HT06}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{Introduction}}{1}}
\citation{HT05}
\citation{Skinner}
\citation{Birch}
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Approximation for hypersurfaces of low degree}}{2}}
\newlabel{section:lowdegree}{{1}{2}}
\newlabel{theo:lowdegree}{{1}{2}}
\citation{PS}
\citation{GHS}
\citation{GHMS}
\newlabel{lemm:Fanononempty}{{3}{3}}
\citation{CTG}
\citation{zhang}
\citation{PS}
\citation{HMP}
\newlabel{sublemm:specialize}{{5}{4}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Ordinary singularities reviewed}}{5}}
\newlabel{sect:ordreview}{{2}{5}}
\newlabel{prop:normalform}{{9}{5}}
\newlabel{rema:constant}{{10}{5}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Degenerate fiber of the resolution when $r=7$}}{6}}
\newlabel{eqn:exctype}{{2.1}{6}}
\citation{HT05}
\citation{kollar}
\citation{HT05}
\citation{HT06}
\citation{HT06}
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Managing free curves}}{7}}
\newlabel{sect:managing}{{3}{7}}
\newlabel{prop:tree}{{13}{7}}
\newlabel{hypo:key}{{14}{7}}
\citation{kollar}
\citation{HT06}
\citation{kollar}
\newlabel{prop:usekey}{{16}{8}}
\newlabel{coro:open}{{17}{8}}
\citation{Na}
\citation{HT06}
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Weak approximation at places with ordinary double points}}{9}}
\newlabel{sect:WAord}{{4}{9}}
\newlabel{theo:main}{{18}{9}}
\newlabel{theo:local}{{19}{9}}
\citation{GHS}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Moving sections from $E_3$ to $E_2$}}{10}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Moving sections from $E_2$ to $E_3$}}{11}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Moving sections within $E_3$}}{12}}
\newlabel{prop:technical}{{22}{12}}
\citation{HT05}
\citation{HT06}
\newlabel{lemm:infinitenear}{{24}{13}}
\citation{HT06}
\citation{HT05}
\citation{Co}
\citation{HT05}
\citation{GH}
\citation{BW}
\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{Applications to cubic hypersurfaces}}{16}}
\newlabel{sect:cubics}{{5}{16}}
\newlabel{theo:cubicmain}{{25}{16}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{Appendix: Recent developments for hypersurfaces of low degree}}{17}}
\citation{dJS}
\bibstyle{amsalpha}
\bibdata{weaksurvey}
\bibcite{Birch}{Bir62}
\bibcite{BW}{BW79}
\bibcite{Co}{Cor96}
\bibcite{CTG}{CTG04}
\bibcite{dJS}{dJS06}
\bibcite{GH}{GH78}
\bibcite{GHMS}{GHMS05}
\bibcite{GHS}{GHS03}
\bibcite{HMP}{HMP98}
\bibcite{HT06}{HT06}
\bibcite{HT05}{HT08}
\bibcite{kollar}{Kol96}
\bibcite{Na}{Nag63}
\bibcite{PS}{PS92}
\bibcite{Skinner}{Ski97}
\bibcite{zhang}{Zha06}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{18}}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{12.7778pt}
\newlabel{tocindent1}{17.77782pt}
\newlabel{tocindent2}{0pt}
\newlabel{tocindent3}{0pt}