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

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.