Abstract Using representations of affine Lie algebras, we describe line bundles on a broad class of contractions of M₀, ₍ 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 KX K X -negative, they exhibit behavior similar to KX K X -negative curves. This reveals a distinguished property of Knudsen’s construction f₊₍ₔ: M₀, ₍ M₀, ₍-₁1. 111pt ₌₀, ₍-₂1. 111ptM₀, ₍-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₊₍ₔ f Knu, as well as further applications.
Daebeom Choi (Tue,) studied this question.