Английская Википедия:Flag bundle
Материал из Онлайн справочника
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:Citation
- Expo. VI, § 4. of Шаблон:Cite book
Шаблон:Algebraic-geometry-stub
- ↑ Here, <math>E_i</math> is a subbundle not subsheaf of <math>E_{i+1}.</math>
