spelled out (here) the example of complex projective bundles of tautological quaternionic line bundles:
]]>Sure, as in the reference given. Discussion of that might naturally go to a page flag bundle.
]]>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.
]]>added a basic note (here) on the splitting off of line bundles in the pullback bundle to a projective bundle
]]>Will do.
]]>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.
]]>I can add some observation about how not every projective bundle is the projectivisation of a vector bundle, etc. in the coming days.
]]>created a minimum at projective bundle
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