Definition
The Hirzebruch surface Σn is the P1 bundle over P1 associated to the sheaf
The notation here means: O(n) is the n-th tensor power of the Serre twist sheaf O(1), the invertible sheaf or line bundle with associated Cartier divisor a single point. The surface Σ0 is isomorphic to P1×P1, and Σ1 is isomorphic to P2 blown up at a point so is not minimal.
Read more about this topic: Hirzebruch Surface
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