Noncommutative rigidity of the moduli stack of stable pointed curves

TL;DR

This paper proves that the second Hochschild cohomology group of the moduli stack of stable n-pointed genus g curves generally vanishes, revealing a form of noncommutative rigidity in these geometric structures.

Contribution

It establishes the vanishing of the second Hochschild cohomology for most cases, advancing understanding of the deformation theory of moduli stacks of curves.

Findings

Vanishing of Hochschild cohomology for most (g,n)

Implication of noncommutative rigidity in moduli stacks

Provides new insights into deformation theory of algebraic stacks

Abstract

We prove that the second Hochschild cohomology group of the moduli stack of stable $n$-pointed genus $g$ curves vanishes for all but finitely many $(g,n)$.