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UID:7358@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20180313T110000
DTEND;TZID=Europe/Paris:20180313T120000
DTSTAMP:20241120T203926Z
URL:https://www.i2m.univ-amu.fr/evenements/moduli-of-curves-with-principal
 -and-spin-bundles-the-singular-locus-via-graph-theory/
SUMMARY: (...): Moduli of curves with principal and spin bundles: the singu
 lar locus via graph theory
DESCRIPTION:: In a series of recent papers\, Chiodo\, Farkas and Ludwig car
 ried out adeep analysis of the singular locus of the moduli space of stabl
 e (twisted) curveswith an $\\ell$-torsion line bundle. They showed that fo
 r $\\ell\\leq 6$ and $\\ell\neq 5$pluricanonical forms extend over any des
 ingularization.This opens the way to a computation of the Kodaira dimensio
 n without desingularizing\,as done by Farkas and Ludwig for $\\ell=2$\,and
  by Chiodo\, Eisenbud\, Farkas and Schreyerfor~$\\ell=3$.We can generalize
  this works in two directions.At first we treat roots of line bundles on t
 he universal curve systematically:we consider the moduli space of curves$C
 $ with a line bundle $L$ such that $L^{\\xx\\ell}\\cong\\omega_C^{\\xx k}$
 .New loci of canonical and non-canonical singularities appearfor any $k\no
 t\\in\\ell\\Z$ and $\\ell>2$\, we provide a set of combinatorial tools all
 owing usto completely describe the singular locus in terms of dual graphs.
 Furthermore\, we treat moduli spaces of curves with a $G$-coverwhere $G$ i
 s any finite group. In particular for $G=S_3$ we approachthe evaluation of
  the Kodaira dimension of the moduli space\, and listthe remaining obstacl
 es to calculate it.
CATEGORIES:Séminaire,Géométrie Complexe
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