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tautological bundle
Definition
- Over \({\mathbf{CP}}^n\), given by \({\mathcal{O}}(-1)\) sending each point \(x\in {\mathbf{CP}}^n\) to the line it spans in \({\mathbf{C}}^{n+1}\).
- Set \({\mathcal{O}}(1) \coloneqq{\mathcal{O}}(-1) {}^{ \vee }\)
- Set \({\mathcal{O}}(n) \coloneqq{\mathcal{O}}(1)^{\otimes n}\)
Exercises
