Tautological bundle
（重定向自Twisting sheaf）
In mathematics, the tautological bundle is a vector bundle occurring over a Grassmannian in a natural tautological way: the fiber of the bundle over a vector space V (a point in the Grassmannian) is V itself. The dual of the tautological bundle has fiber over a vector space V that is the dual vector space of V. In the case of projective space the tautological bundle is known as the tautological line bundle.