complex line bundle造句

There is a universal bundle for real line bundles, and a universal bundle for complex line bundles.
In an analogous way, the complex projective space "'CP "' " carries a universal complex line bundle.
In topology, the complex projective space plays an important role as a classifying space for complex line bundles : families of complex lines parametrized by another space.
In particular, all ( " n, 0 " )-forms are related locally by multiplication by a complex function and so they form a complex line bundle.
The total space of this bundle "'P "'( " E " ) is equipped with its tautological complex line bundle, that we denote ?, and the first Chern class
It's difficult to find complex line bundle in a sentence. 用complex line bundle造句挺难的

In algebraic geometry, this classification of ( isomorphism classes of ) complex line bundles by the first Chern class is a crude approximation to the classification of ( isomorphism classes of ) holomorphic line bundles by linear equivalence classes of divisors.
In the equivariant case, this translates to : the equivariant first Chern gives a bijection between the set of all isomorphism classes of equivariant complex line bundles and H ^ 2 _ G ( M; \ mathbb { Z } ).
In the non-equivariant case, the first Chern class can be viewed as a bijection between the set of all isomorphism classes of complex line bundles on a manifold " M " and H ^ 2 ( M; \ mathbb { Z } ).
If " E " has a hermitian metric, then the conjugate bundle is isomorphic to the dual bundle E ^ * = \ operatorname { Hom } ( E, \ mathcal { O } ) through the metric, where we wrote \ mathcal { O } for the trivial complex line bundle.