# Genus of complex projective space

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 $N$?

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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.