The Picard group of the moduli space of curves with level structures
Author
Putman, Andrew
Date
2012Abstract
For 4 - L and g large, we calculate the integral Picard groups of the moduli spaces of curves and principally
polarized abelian varieties with level L structures. In particular, we determine the divisibility properties
of the standard line bundles over these moduli spaces and we calculate the second integral cohomology
group of the level L subgroup of the mapping class group (in a previous paper, the author determined this
rationally). This entails calculating the abelianization of the level L subgroup of the mapping class group,
generalizing previous results of Perron, Sato, and the author. Finally, along the way we calculate the first
homology group of the mod L symplectic group with coefficients in the adjoint representation.
Citation
Published Version
Type
Journal article