  Given a positive integer $n$ the $k$-fold divisor function $d_k(n)$ equals
the number of ordered $k$-tuples of positive integers whose product equals $n$.
In this article we study the variance of sums of $d_k(n)$ in short intervals
and establish asymptotic formulas for the variance of sums of $d_k(n)$ in short
intervals of certain lengths for $k=3$ and for $k \ge 4$ under the assumption
of the Lindel\"of hypothesis.
