Mori's program for $\bar{M}_{0,6}$ with symmetric divisors

TL;DR

This paper completes Mori's program for the moduli space of stable six-pointed rational curves using symmetric divisors and provides an alternative proof for the Mori's program of genus two stable curves.

Contribution

It advances the understanding of Mori's program for specific moduli spaces and offers a new proof for genus two curves.

Findings

Complete Mori's program for ,6 with symmetric divisors

Alternative proof for Mori's program of genus two stable curves

Enhanced understanding of the birational geometry of these moduli spaces

Abstract

We complete Mori's program with symmetric divisors for the moduli space of stable six pointed rational curves. As an application, we give an alternative proof of the complete Mori's program of the moduli space of genus two stable curves, done by Hassett.