I am currently reading the section on the Dolbeault cohomology in Griffiths & Harris Principles of Algebraic Geometry and am having trouble understanding some problems.
It is obvious that $${ H }^{ q }\left( \mathbb{ C }^{ n },\mathcal{O} \right) =0 ,\qquad q>0$$ according to the the $\bar{\partial}$-Poincaré lemma and the Dolbeault cohomology.
And more generally $${ H }^{ q }\left( { \left( \mathbb{ C }\right) }^{ k }\times { \left( {\mathbb{ C }}^{ \ast } \right) }^{ l },{ O } \right) =0,\qquad q>0$$ since $\mathbb{ C }^{ n }$ is contractible, moreover, we see that $${ H }^{ q }\left( \mathbb{ C }^{ n },\mathbb{ Z } \right) =0, \qquad q>0$$
I am having trouble understanding the last two equations. Any hlep would be appreciated. Thanks in advance.