The complex projective line is isomorphic to the 2-sphere, and so, has genus $0$. Does this result for all $CP^N$, that is, is the genus of $CP^N$ equal to $0$, for all $N$?



Genus of complex projective space
The geometric genus (the dimension of the space of global sections of the
canonical sheaf) of projective $n$-space is zero. See Hartshorne II.8.


