$sl_n$ level 1 conformal blocks divisors on $\bar{M}_{0,n}$

TL;DR

This paper investigates $sl_n$ level 1 conformal blocks divisors on $ar{M}_{0,n}$, demonstrating they generate extremal rays in the symmetric nef cone and induce birational contractions factoring through Hassett's weighted moduli spaces.

Contribution

It provides explicit computations of these divisors' classes and establishes their role in the birational geometry of $ar{M}_{0,n}$, linking conformal blocks to moduli space contractions.

Findings

Divisors generate extremal rays in the symmetric nef cone.

Divisors induce birational contractions of $ar{M}_{0,n}$.

Contractions factor through Hassett's weighted moduli spaces.

Abstract

We study a family of semiample divisors on the moduli space $\bar{M}_{0,n}$ that come from the theory of conformal blocks for the Lie algebra $sl_n$ and level 1. The divisors we study are invariant under the action of $S_n$ on $\bar{M}_{0,n}$. We compute their classes and prove that they generate extremal rays in the cone of symmetric nef divisors on $\bar{M}_{0,n}$. In particular, these divisors define birational contractions of $\bar{M}_{0,n}$, which we show factor through reduction morphisms to moduli spaces of weighted pointed curves defined by Hassett.