Projective varietes, linear systems and vector bundles PDF

If the structure group of a vector bundle is reducible to \({GL(n,\mathbb{K})^{e}}\), then it is called an orientable bundle; all complex vector bundles are orientable, so orientability usually refers to real vector bundles.The tangent bundle of \({M}\) (formally defined in an upcoming section) is then orientable iff \({M}\) is orientable.On a pseudo-Riemannian manifold \({M}\), the structure