2016/11/01 by Sepideh Tashvighi, Tashvighi, Sepideh
Mathematics · #14H10 #14H15 #14H20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1611.00245
openalex publication_date 2016/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We further analyze the moduli space of stable curves with level structure provided by Chiodo and Farkas in \citeAA. Their result builds upon Harris and Mumford analysis of the locus of singularities of the moduli space of curves and shows in particular that for levels 2, 3, 4, and 6 the locus of noncanonical singularities is completely analogous to the locus described by Harris and Mumford, it has codimension 2 and arises from the involution of elliptic tails carrying a trivial level structure. For the remaining levels (5, 7, and beyond), the picture also involves components of higher codimension. We show that there exists a component of codimension 3 for levels ℓ=5 and ℓ\geqslant 7 with the only exception of level 12. We also show that there exists a component of codimension 4 for ℓ=12.