Английская Википедия:Flag bundle

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In algebraic geometry, the flag bundle of a flag[1]

<math>E_{\bullet}: E = E_l \supsetneq \cdots \supsetneq E_1 \supsetneq 0</math>

of vector bundles on an algebraic scheme X is the algebraic scheme over X:

<math>p: \operatorname{Fl}(E_{\bullet}) \to X</math>

such that <math>p^{-1}(x)</math> is a flag <math>V_{\bullet}</math> of vector spaces such that <math>V_i</math> is a vector subspace of <math>(E_i)_x</math> 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.

References

Шаблон:Reflist

Шаблон:Algebraic-geometry-stub

  1. Here, <math>E_i</math> is a subbundle not subsheaf of <math>E_{i+1}.</math>