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 \(\mathcal {M}_g\).
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