Geodesic
Singularities of the moduli space of level curves
Journal of the European Mathematical Society, Tome 19 (2017) no. 3, pp. 603-658 Cet article a éte moissonné depuis la source EMS Press

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We describe the singular locus of the compactification of the moduli space Rg,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 Rg,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.
DOI : 10.4171/jems/677
Classification : 14-XX
Keywords: Moduli of curves 
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     author = {Alessandro Chiodo and Gavril Farkas},
     title = {Singularities of the moduli space of level curves},
     journal = {Journal of the European Mathematical Society},
     pages = {603--658},
     year = {2017},
     volume = {19},
     number = {3},
     doi = {10.4171/jems/677},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/677/}
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Alessandro Chiodo; Gavril Farkas. Singularities of the moduli space of level curves. Journal of the European Mathematical Society, Tome 19 (2017) no. 3, pp. 603-658. doi: 10.4171/jems/677

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