Good moduli spaces of A_r-stable curves

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• Michele Pernice KTH
• Wednesday 26 February 2025, 14:15-15:15
• CMS MR13.

If you have a question about this talk, please contact Mark Gross.

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 A_r-singularities, which we call A_r-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 A_r-stable curves. We will explain the choice of the open by showing what the obstructions to S-completeness and Theta-reductivity are for the stack of A_r-stable curves. This is an on-going project with Davide Gori and Ludvig Modin.

This talk is part of the Algebraic Geometry Seminar series.

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