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Jul 11, 2011 at 16:57 comment added Francesco Polizzi Since $P_n$ is not a base point of $|D|$, there is a section of $H^0(D)$ that does not vanish in $P_n$. So the inclusion $H^0(D-P_n) \subset H^0(D)$ is strict. On the other hand, imposing the passage through a point is at most one linear condition, so $H^0(D-P_n)$ has codimension exactly $1$ in $H^0(D)$.
Jul 11, 2011 at 16:48 answer added Mike Skirvin timeline score: 1
Jul 11, 2011 at 16:35 history asked phil CC BY-SA 3.0