On Koszulity in homology of moduli spaces of stable n-pointed curves of genus zero

TL;DR

This paper proves the Koszulity property of the homology of moduli spaces of stable n-pointed genus zero curves for n=5 and 6, using algebraic and combinatorial methods to establish new results in this area.

Contribution

It demonstrates Koszulity for the homology of bar{M}_{0,n} for n=5 and 6, including explicit potential functions and criteria applications.

Findings

Proves Koszulity for n=5 using Keel's presentation and Priddy criterion.

Establishes potentiality and Koszulity for bar{M}_{0,6}.

Provides explicit potential expression for n=6.

Abstract

We prove Koszulity of the homology of the of moduli spaces of stable n-pointed curves of genus zero $\overline{M}_{0,n}$ for $n=5$, using its presentation due to Keel and the Priddy criterion of Koszulity. For $n=6 $ we establish that $\overline{M}_{0,6}^!$ is potential, find the expression for the potential, and based on that prove that it is Koszul.