New answers tagged blow-ups
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Three-dimensional analogues of Hirzebruch surfaces
The 3-dimensional analogues should be $\mathbb{P}(O(a)\oplus O(b)\oplus O(c))$, yes. These are exactly the $\mathbb{P}^2$-bundles over $\mathbb{P}^1$.
In general, any projectivization of a vector ...
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