Veronese quotient models of ̅M0,n and conformal blocks

Abstract

The moduli space M0;n of Deligne-Mumford stable n-pointed rational curves admits morphisms to spaces recently constructed by Giansiracusa, Jensen, and Moon that we call Veronese quotients. We study divisors on M0;n associated to these maps and show that these divisors arise as rst Chern classes of vector bundles of conformal blocks. 0;n that receive morphisms from M0;n. From the perspective of Mori theory, this is tantamount to describing cer- tain semi-ample divisors on M0;n. This work is concerned with two recent constructions that each yield an abundance of such semi-ample divisors on M0;n, and the relationship between them. The rst comes from Geometric Invariant Theory (GIT), while the second from conformal eld theory. There are new natural birational models of M0;n obtained via GIT which are moduli spaces of pointed rational normal curves of a