Rational Contractions of Fiber Type on $\overline{M}_{0,6}$

TL;DR

This paper introduces a new algorithm to analyze the cone of effective divisors on $ar{M}_{0,6}$, identifying initial rational contractions of fiber type and their associated nef curve faces.

Contribution

It develops a novel algorithm for verifying the cone of effective divisors and applies it to $ar{M}_{0,6}$ to identify specific rational contractions of fiber type.

Findings

Identified initial rational contractions of fiber type on $ar{M}_{0,6}$.

Developed a new algorithm for cone verification on Mori dream spaces.

Algorithm successfully identifies faces of the nef cone related to these contractions.

Abstract

We identify a set of initial rational contractions of fiber type on $\overline{M}_{0,6}$. Our proof uses a new algorithm we develop for verifying descriptions of the cone of effective divisors on varieties without elementary rational contractions of fiber type. On Mori dream spaces, our algorithm identifies faces of the cone of nef curves associated to initial rational contractions of fiber type.