• Corpus ID: 54017607

Singularities of moduli of curves with a universal root

  title={Singularities of moduli of curves with a universal root},
  author={Mattia Galeotti},
  journal={arXiv: Algebraic Geometry},
In a series of recent papers, Chiodo, Farkas and Ludwig carry out a deep analysis of the singular locus of the moduli space of stable (twisted) curves with an $\ell$-torsion line bundle. They show that for $\ell\leq 6$ and $\ell\neq 5$ pluricanonical forms extend over any desingularization. This allows to compute the Kodaira dimension without desingularizing, as done by Farkas and Ludwig for $\ell=2$, and by Chiodo, Eisenbud, Farkas and Schreyer for $\ell=3$. Here we treat roots of line bundles… 

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