Let $X$ be an algebraic surface, $H$ be a very ample divisor. Suppose $C\in|H|$, such that $\deg_C(D)=DC<0$, with some divisor $D$.
Q: Why $h^0(C,D|_C)=0$?
Negative Intersection and Vanishing global section
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algebraic-geometry
intersection-theory
divisors-algebraic-geometry
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0Isn't it just the fact that for any divisor $D$ with negative degree on a curve, $h^0(C,D)=0$ ? (Because a rational function can't have more zeros than it has poles) – 2017-02-19