Flag bundle

In algebraic geometry, the flag bundle of a flag
of vector bundles on an algebraic scheme "X" is the algebraic scheme over "X":
such that formula_3 is a flag formula_4 of vector spaces such that formula_5 is a vector subspace of formula_6 of dimension "i".
If "X" is a point, then a flag bundle is a flag variety and if the length of the flag is one, then it is the Grassmann bundle; hence, a flag bundle is a common generalization of these two notions.
Construction.
A flag bundle can be constructed inductively.