Moduli space of pairs over projective stacks

الأصل · EN

Let a projective stack over an algebraically closed field k of characteristic 0. Let be a generating sheaf over and 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 Γ⊗→ where Γ is a finite dimensional k vector space and is a coherent sheaf over. 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.