Gromov–Witten and quasimap invariants of toric varieties – a geometric perspective

Given F a coherent sheaf on a Noetherian integral algebraic stack P, we give two constructions of stacks P' equipped with birational morphisms p from P' to P such that p*F is simpler: in the Rossi construction, the torsion-free part of p*F is locally free; in the Hu–Li diagonalization construction, the associated abelian cone C(p*F) is a union of vector bundles. We use these constructions to define reduced Gromov–Witten invariants of complete intersections in all genera.