  We initiate the study of applying the Combinatorial Nullstellensatz to the
DP-coloring of graphs even though, as is well-known, the Alon-Tarsi theorem
does not apply to DP-coloring. We define the notion of good covers of prime
order which allows us to apply the Combinatorial Nullstellensatz to
DP-coloring. We apply these tools to DP-coloring of the cones of certain
bipartite graphs and uniquely 3-colorable graphs. We also extend a result of
Akbari, Mirrokni, and Sadjad (2006) on unique list colorability to the context
of DP-coloring. We establish a sufficient algebraic condition for a graph $G$
to satisfy $\chi_{DP}(G) \leq 3$, and we completely determine the DP-chromatic
number of squares of all cycles.
