= Rational normal scroll
{title2=$\mathbb F(a_1,\ldots,a_n)=\mathbb P_{\mathbb P^1}(\bigoplus_i\mathcal O(a_i))$}
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= Scroll
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= Rational scroll
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For this smooth <projective bundle>, put $L=\pi^*\mathcal O_{\mathbb P^1}(1)$ and $M=\mathcal O_{\mathbb F}(1)$, using <projectivization by quotients>. If every $a_i>0$, the complete system $|M|$ embeds it as a rational normal scroll. If every $a_i\ge0$, the same system defines a scroll image which may be singular. Allowing arbitrary integers gives an abstract scroll; a common twist makes an embedding available. Its <intersection numbers> are $L^2=0$, $LM^{n-1}=1$, $M^n=\sum_i a_i$, and its <canonical divisor> is $-nM+(\sum_i a_i-2)L$.
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