A projective bundle associated with a vector bundle 
of rank 
on a variety 
has projective-space fibers of dimension 
. In the subspace convention, 
parametrizes one-dimensional subspaces
of the fibers of 
.
Locally where 
is trivial, it is 
.
Another common convention parametrizes one-dimensional quotients and replaces 
by its dual.
For a smooth projective base, descendant Gromov-Witten invariants can be studied on this total space.
