The category of perverse sheaves, Perv_X, on a stratified space X plays an
important role in the Intersection cohomology of Goresky-MacPherson and on the theory of
D-modules. It is defined as a subcategory of the derived category of
sheaves. Hence a usual complaint is that there are not very concrete
objects. A lot of work has been done to describe Perv_X more explicitly.
Hence many methods had been develop to describe Perv_X as a category of
quiver representations. An important property of perverse sheaves is that they can be viewed as a
stack, it means that a perverse sheaf can be defined up to isomorphism from
the data of perverse sheaves on an open cover of X plus some glueing data.
In this talk we show how the theory of stacks and more precisely the
notion of constructible stacks can be used in order to glue a description
due to Galligo, Granger and Maisonobe of the category Perv_X when X is C^n
stratified by a normal crossing stratification. Thanks to this we will
obtain a description of Perv_X on smooth toric varieties stratified by the
torus action.