Tautological bundle

In the mathematical field of the topology and geometry of the beam is at a tautological projective space an object that associates each point of the line from which it arose.

Definition

The tautological bundle over a projective space to a vector space is the line bundle whose fiber at a point of the corresponding one-dimensional subspace of. It is a sub- bundle of the trivial bundle.

Analog can be defined on the Grassmann - dimensional subspaces of a vector space, the tautological bundle; it is a vector bundle of rank.

Properties

• The Picardgruppe the line bundle on is infinite cyclic, and the tautological bundle is a producer.
• The sheaf of sections of the tautological bundle is the inverse of Serres Twistinggarbe.