Andreini, Elena2012-01-232012-01-232011-05-27https://openscience.sissa.it/handle/1963/5263Let $\clX$ a projective stack over an algebraically closed field $k$ of characteristic 0. Let $\clE$ be a generating sheaf over $\clX$ and $\clO_X(1)$ a polarization of its coarse moduli space $X$. We define a notion of pair which is the datum of a non vanishing morphism $\Gamma\otimes\clE\to \clF$ where $\Gamma$ is a finite dimensional $k$ vector space and $\clF$ is a coherent sheaf over $\clX$. We construct the stack and the moduli space of semistable pairs. The notion of semistability depends on a polynomial parameter and it is dictated by the GIT construction of the moduli space.enPreprintMAT/03 GEOMETRIA