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Mar 23, 2013 at 13:56 comment added Dmitri Panov This is not true, consider for example a divisor $D$ on a surface that is a wheel of $\mathbb P^1$'s, i.e, each $\mathbb P^1$ intersects two neighbouring $\mathbb P^1$'s. Then $\pi_1(D)=\mathbb Z$, so $H^1(D)=\mathbb Z$.
Mar 23, 2013 at 13:00 history asked nnccdd CC BY-SA 3.0