In algebraic geometry, the moduli stack of rank-n vector bundles Vectn is the stack parametrizing vector bundles (or locally free sheaves) of rank n over some reasonable spaces.
It is a smooth algebraic stack of the negative dimension − n 2 {\displaystyle -n^{2}} . Moreover, viewing a rank-n vector bundle as a principal G L n {\displaystyle GL_{n}} -bundle, Vectn is isomorphic to the classifying stack B G L n = [ pt / G L n ] . {\displaystyle BGL_{n}=[{\text{pt}}/GL_{n}].}