Michele Pernice (KTH Stoccolma)

Abstract: The search for alternative compactifications of the moduli space of smooth curves has been central in the panorama of moduli spaces and a possible way to construct such compactifications is allowing curves with worse-than-nodal singularities. Curves with -singularities, which we call -stable, naturally appear in the literature as a possible choice. This project focuses on proving the existence of the good moduli space of a suitable open of the moduli stack of -stable curves. We will explain the choice of the open by showing what the obstructions to -completeness and -reductivity are for the stack of -stable curves. This is an on-going project with Davide Gori and Ludvig Modin.