# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 28th 2017

created a minimum at projective bundle

• CommentRowNumber2.
• CommentAuthorDavidRoberts
• CommentTimeMay 29th 2017

I can add some observation about how not every projective bundle is the projectivisation of a vector bundle, etc. in the coming days.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 29th 2017

Thanks. When you do that, you should also state the definition (I suppose fiber bundle with a projective space as the typical fiber) because at the moment the entry only talks about projectivisation of vector bundles.

• CommentRowNumber4.
• CommentAuthorDavidRoberts
• CommentTimeMay 29th 2017

Will do.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeDec 30th 2020
• (edited Dec 30th 2020)

added a basic note (here) on the splitting off of line bundles in the pullback bundle to a projective bundle

• CommentRowNumber6.
• CommentAuthorTodd_Trimble
• CommentTimeDec 30th 2020

I think also the complete splitting could be executed in one shot by pulling back to a “flag bundle” associated to a vector bundle. I’m not sure what terminology people use though.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeDec 30th 2020

Sure, as in the reference given. Discussion of that might naturally go to a page flag bundle.

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeDec 31st 2020

spelled out (here) the example of complex projective bundles of tautological quaternionic line bundles:

$\array{ P_{\mathbb{C}} \big( \mathcal{L}_{{}_{\mathbb{H}P^n}} \big) && \simeq && \mathbb{C}P^{2n+1} \\ & \searrow && \swarrow_{ \mathrlap{ v \cdot \mathbb{C}^\times \,\mapsto\, v \cdot \mathbb{H}^\times } } \\ && \mathbb{H}P^n }$