\contentsline {section}{\numberline {0}Introduction}{2}
\contentsline {section}{\numberline {1}Generalities}{4}
\contentsline {subsection}{\numberline {1.1}Singularities of pairs and effective cones}{4}
\contentsline {subsection}{\numberline {1.2}Integral points}{6}
\contentsline {subsection}{\numberline {1.3}Computing effective cones}{7}
\contentsline {section}{\numberline {2}Construction of resolutions}{8}
\contentsline {subsection}{\numberline {2.1}Binary forms and ${\rm SL}_2$-orbit closures}{8}
\contentsline {subsection}{\numberline {2.2}Moduli spaces}{9}
\contentsline {subsection}{\numberline {2.3}Resolution for the full moduli space}{11}
\contentsline {subsection}{\numberline {2.4}Resolution of the generic orbit}{12}
\contentsline {section}{\numberline {3}Verification of exponents}{15}
\contentsline {subsection}{\numberline {3.1}Explicit basis of ${\rm Pic}(Y_{\alpha })$}{15}
\contentsline {subsection}{\numberline {3.2}Computation of the effective cone}{16}
\contentsline {subsection}{\numberline {3.3}Proof of the main theorem}{16}
\contentsline {section}{\numberline {4}The invariant effective cone}{18}
\contentsline {section}{\numberline {5}Final remarks}{23}