Line bundles on contractions of $$\overline{\textrm{M}}_{0,n}$$ via coinvariant divisors

Abstract Using representations of affine Lie algebras, we describe line bundles on a broad class of contractions of $$\overline{\textrm{M}}_{0,n}$$ M ¯ 0 , n , the moduli space of stable n -pointed rational curves, and show a variant of the cone and contraction theorem for these morphisms. These include the celebrated constructions of Kapranov, Keel, and Knudsen. Our main result suggests that while many so-called F-curves are not $$K_X$$ K X -negative, they exhibit behavior similar to $$K_X$$ K X -negative curves. This reveals a distinguished property of Knudsen’s construction $$f_{\textrm{Knu}}:\overline{\textrm{M}}_{0,n}\rightarrow \overline{\textrm{M}}_{0,n-1}\hspace{1.111pt}{\times }_{\overline{\textrm{M}}_{0,n-2}}\hspace{1.111pt}\overline{\textrm{M}}_{0,n-1}$$ f Knu : M ¯ 0 , n → M ¯ 0 , n - 1 × M ¯ 0 , n - 2 M ¯ 0 , n - 1 , allowing for the classification of all possible factorizations of $$f_{\textrm{Knu}}$$ f Knu , as well as further applications.