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Good moduli space of $A_r$-stable curves

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EMGW05 - Moduli stacks and enumerative geometry

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 Isaac Newton Institute Seminar Series series.

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Hinsley Lecture Series Lecture Theatre O, Engineering Department, Trumpington Street CMS MR 14, Monday 12 November 4 pm

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