Mori's program for the moduli space of pointed stable rational curves

TL;DR

This paper establishes the relationship between the log canonical models of moduli spaces of pointed stable rational curves and Hassett's weighted moduli spaces, assuming the F-conjecture, and generalizes Simpson's theorem to boundary weight cases.

Contribution

It proves the equivalence of the log canonical model with Hassett's moduli space under the F-conjecture and extends Simpson's theorem to boundary weight cases.

Findings

Under the F-conjecture, the log canonical model matches Hassett's moduli space.

For boundary weights, the birational model is a GIT quotient of a product of projective lines.

Generalizes Simpson's theorem to include boundary weight cases.

Abstract

We prove that, assuming the F-conjecture, the log canonical model of the pair $(\bar{M}_{0,n}, \sum a_i \psi_i)$ is the Hassett's moduli space of weighted pointed stable rational curves without any modification of weight coefficients. For the boundary weight cases, we prove that the birational model is the GIT quotient of the product of the projective lines. This is a generalization of Simpson's theorem for symmetric weight cases.