  We show $\overline{\mathcal{M}}_{10,10}$ and $\mathcal{F}_{11,9}$ have
Kodaira dimension zero. Our method relies on the construction of a number of
curves via nodal Lefschetz pencils on blown-up $K3$ surfaces. The construction
further yields that any effective divisor in $\overline{\mathcal{M}}_{g}$ with
slope $<6+(12-\delta)/(g+1)$ must contain the locus of curves that are the
normalization of a $\delta$-nodal curve lying on a $K3$ surface of genus
$g+\delta$.
