\contentsline {section}{\tocsection {}{Lecture 0}{Introduction: curves}}{1}
\contentsline {subsection}{\tocsubsection {}{0.1}{Closed curves}}{2}
\contentsline {subsection}{\tocsubsection {}{0.2}{Open curves}}{3}
\contentsline {subsection}{\tocsubsection {}{0.3}{Faltings implies Siegel}}{6}
\contentsline {subsection}{\tocsubsection {}{0.4}{Function field case}}{8}
\contentsline {section}{\tocsection {}{Lecture 1}{Kodaira dimension}}{9}
\contentsline {subsection}{\tocsubsection {}{1.1}{Iitaka dimension}}{9}
\contentsline {subsection}{\tocsubsection {}{1.2}{Uniruled varieties and rationally connected fibrations}}{16}
\contentsline {subsection}{\tocsubsection {}{1.3}{Geometry and arithmetic of the Iitaka fibration}}{21}
\contentsline {subsection}{\tocsubsection {}{1.4}{Lang's conjecture}}{22}
\contentsline {subsection}{\tocsubsection {}{1.5}{Uniformity of rational points.}}{24}
\contentsline {subsection}{\tocsubsection {}{1.6}{The search for an arithmetic dichotomy}}{25}
\contentsline {subsection}{\tocsubsection {}{1.7}{Logarithmic Kodaira dimension and Lang-Vojta conjectures}}{27}
\contentsline {section}{\tocsection {}{Lecture 2}{Campana's program}}{29}
\contentsline {subsection}{\tocsubsection {}{2.1}{One dimensional Campana constellations}}{29}
\contentsline {subsection}{\tocsubsection {}{2.2}{Higher dimensional Campana constellations}}{37}
\contentsline {subsection}{\tocsubsection {}{2.3}{Firmaments supporting constellations and integral points}}{45}
\contentsline {subsubsection}{\tocsubsubsection {}{2.3.1}{Toroidalizing a morphism}}{48}
\contentsline {section}{\tocsection {}{Lecture 3}{The minimal model program}}{56}
\contentsline {subsection}{\tocsubsection {}{3.1}{Cone of curves}}{56}
\contentsline {subsection}{\tocsubsection {}{3.2}{Bend and break}}{56}
\contentsline {subsection}{\tocsubsection {}{3.3}{Cone theorem}}{56}
\contentsline {subsection}{\tocsubsection {}{3.4}{The minimal model program}}{56}
\contentsline {section}{\tocsection {}{Lecture 4}{Vojta, Campana and $abc$}}{56}
\contentsline {subsection}{\tocsubsection {}{4.1}{Heights: local and global}}{56}
\contentsline {subsection}{\tocsubsection {}{4.2}{Vojta's conjecture}}{56}
\contentsline {subsection}{\tocsubsection {}{4.3}{Vojta and $abc$}}{56}
\contentsline {subsection}{\tocsubsection {}{4.4}{Campana and $abc$}}{56}
\contentsline {subsection}{\tocsubsection {}{4.5}{Vojta and Campana}}{56}