Solution
= Solution
The <Hodge decomposition theorem for compact Kähler manifolds> states
$$
H^k_{dR}(X;\mathbb C)=\bigoplus_{p+q=k}H^{p,q}_{\bar\partial}(X),
$$
with each summand represented uniquely by harmonic forms of type $(p,q)$. Part b shows that these are precisely the constant-coefficient forms $dz_I\wedge d\overline z_J$. Therefore the <Hodge number>[Hodge numbers] of a complex $n$-torus are
$$
h^{p,q}(X)=\binom np\binom nq.
$$