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SUMMARY:Good moduli space of  $A_r$-stable curves - Michele Pernice (KTH -
  Royal Institute of Technology)
DTSTART:20240618T130000Z
DTEND:20240618T134000Z
UID:TALK217696@talks.cam.ac.uk
DESCRIPTION:The search for alternative compactifications of the moduli spa
 ce 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 w
 e call $A_r$-stable\, naturally appear in the literature as a possible cho
 ice. This project focuses on proving the existence of the good moduli spac
 e of a suitable open of the moduli stack of $A_r$-stable curves. We will e
 xplain the choice of the open by showing what the obstructions to $S$-comp
 leteness and $\\Theta$-reductivity are for the stack of $A_r$-stable curve
 s. This is an on-going project with Davide Gori and Ludvig Modin.
LOCATION:Seminar Room 1\, Newton Institute
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