Skip to main content
MathOverflow

Return to Question

added 5 characters in body
Source Link
Partha
Partha
  • 954
  • 6
  • 16

It's not hard to see the following fact: the circle bundle of the tautological line bundle $\mathcal{O}(-1)\rightarrow \mathbb{CP}^n$ is $S^{2n+1}$, the unit sphere inside $C^{n+1}.$ I want to see some similar identification of the circle bundle of the canonical line bundle $\mathcal{O}(-n-1)$, is it a Lens space $S^{2n+1}/\mathbb{Z}_{2n+1}$?

It's not hard to see the following fact: the circle bundle of the tautological line bundle $\mathcal{O}(-1)\rightarrow \mathbb{CP}^n$ is $S^{2n+1}$, the unit sphere inside $C^{n+1}.$ I want to see some similar identification of the circle bundle of the canonical bundle $\mathcal{O}(-n-1)$, is it a Lens space $S^{2n+1}/\mathbb{Z}_{2n+1}$?

It's not hard to see the following fact: the circle bundle of the tautological line bundle $\mathcal{O}(-1)\rightarrow \mathbb{CP}^n$ is $S^{2n+1}$, the unit sphere inside $C^{n+1}.$ I want to see some similar identification of the circle bundle of the canonical line bundle $\mathcal{O}(-n-1)$, is it a Lens space $S^{2n+1}/\mathbb{Z}_{2n+1}$?

Source Link
Partha
Partha
  • 954
  • 6
  • 16

Identifying the circle bundle of the canonical line bundle $\mathcal{O}(-n-1)$ over a projective space $\mathbb{CP}^n$

It's not hard to see the following fact: the circle bundle of the tautological line bundle $\mathcal{O}(-1)\rightarrow \mathbb{CP}^n$ is $S^{2n+1}$, the unit sphere inside $C^{n+1}.$ I want to see some similar identification of the circle bundle of the canonical bundle $\mathcal{O}(-n-1)$, is it a Lens space $S^{2n+1}/\mathbb{Z}_{2n+1}$?