The automorphisms group of $\overline{M}_{0,n}$

TL;DR

This paper characterizes fiber type morphisms between moduli spaces of pointed rational curves, proving that the automorphism group of rac{rac{0,n0,n0,n} is the symmetric group on n elements for n 0 5.

Contribution

It establishes that all fiber type morphisms are forgetful maps and determines the automorphism group of rac{rac{0,n0,n0,n} as the symmetric group for n 0 5.

Findings

Only forgetful maps are fiber type morphisms.

Automorphism group of rac{rac{0,n0,n0,n} is the permutation group for n 0 5.

Results rely on Kapranov's description of moduli spaces.

Abstract

In this paper we study fiber type morphisms between moduli spaces of pointed rational curves. Via Kapranov's description we are able to prove that the only such morphisms are forgetful maps. This allow us to show that the Automorphism group of $\overline{M}_{0,n}$ is the permutation group on $n$ elements as soon as $n\geq 5$.