Singularities of the moduli space of level curves

2012/05/01 by Chiodo, Alessandro, Farkas, Gavril
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1205.0201

Abstract

We describe the singular locus of the compactification of the moduli space R_g,l of curves of genus g paired with an l-torsion point in their Jacobian. Generalising previous work for l≤ 2, we also describe the sublocus of noncanonical singularities for any positive integer l. For g≥ 4 and l=3,4, 6, this allows us to provide a lifting result on pluricanonical forms playing an essential role in the computation of the Kodaira dimension of R_g,l: for those values of l, every pluricanonical form on the smooth locus of the moduli space extends to a desingularisation of the compactified moduli space.

Related

• Low Codimension Strata of the Singular Locus of Moduli of Level Curves
• On the geometry of the moduli space of spin curves
• The Kodaira classification of the moduli space of pointed curves in genus 3
• The Geometry of the Moduli Space of Curves of Genus 23
• The Kodaira dimension of moduli spaces of curves with marked points, II