Picard group of moduli of curves of low genus in positive characteristic

Abstract

We compute the Picard group of the moduli stack of smooth curves of genus $g$ for $3\le g\le 5$, using methods of equivariant intersection theory. We base our proof on the computation of some relations in the integral Chow ring of certain moduli stacks of smooth complete intersections. As a byproduct, we compute the cycle classes of some divisors on ${\mathcal{M}}_g$.

19 pages, to appear in Manuscripta Mathematica. Comments are welcome!