  We compute the class of the closure of the locus of canonical divisors in the
projectivization of the Hodge bundle $\mathbb{P}\overline{\mathcal{H}}_g$ over
$\overline{\mathcal{M}}_g$ which have a zero at a Weierstrass point. We also
show that the strata of canonical and bicanonical divisors with a double zero
span extremal rays of the respective pseudoeffective cones.
