Seminari del Dipartimento
Geometria Moduli of curves with principal and spin bundles: singularities and global geometry Mattia Galeotti 26-10-2017 - 15:00 Largo San Leonardo Murialdo,1 - Pal.C - AULA 211
In a series of recent papers, Chiodo, Farkas and Ludwig carried out a deep analysis of the singular locus of the moduli space of stable (twisted) curves with an l-torsion line bundle. They showed that for l ≤ 6 and different from 5 pluricanonical forms extend over any desingularization. This opens the way to a computation of the Kodaira dimension without desingularizing, as done by Farkas and Ludwig for l = 2, and by Chiodo, Eisenbud, Farkas and Schreyer for l = 3. We can generalize this works in two directions. At first we treat roots of line bundles on the universal curve systematically: we consider the moduli space of curves C with a line bundle L such that L^l is isomorphic to a chosen power of the canonical bundle. New loci of canonical and non-canonical singularities appear and we provide a set of combinatorial tools allowing us to completely describe the singular locus in terms of dual graphs. |