  Affine superspace $\mathbb{C}^{1 \mid n}$ has a single bosonic coordinate $z$
and $n$ fermionic coordinates $\theta_1, \dots, \theta_n$. Let $M$ be the
supertorus obtained by quotienting $\mathbb{C}^{1 \mid n}$ by the abelian group
generated by the maps $S: (z,\theta_1, \dots, \theta_n) \mapsto (z + 1,
\theta_1, \dots, \theta_n)$ and $T: (z, \theta_1, \dots, \theta_n) \mapsto (z +
t, \theta_1 + \alpha_1, \dots, \theta_n + \alpha_n)$ where $t \in \mathbb{C}$
has positive imaginary part and $\alpha_1, \dots, \alpha_n$ are independent
fermionic parameters. We compute the zeroth and first cohomology groups of the
structure sheaf $\mathcal{O}$ of $M$ as doubly graded $\mathfrak{S}_n$-modules,
exhibiting an instance of Serre duality between these groups. We use skein
relations and noncrossing matchings to give a combinatorial presentation of
$H^0(M,\mathcal{O})$ in terms of generators and relations.
