Line bundles on Contractions of $\overline{\rm{M}}_{0,n}$ via Coinvariant Divisors

Daebeom Choi

Paper

Line bundles on Contractions of $\overline{\rm{M}}_{0,n}$ via Coinvariant Divisors

Abstract

Using representations of vertex operator algebras, we describe the line bundles on a wide range of contractions of

, the moduli space of stable

-pointed rational curves, by proving a stronger version of the 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

-negative, they exhibit behavior similar to

-negative curves. This reveals for instance, a distinguished property of Knudsen's construction

, allowing for the classification of all possible factorizations of

, as well as further applications, and generalizations.