Two desingularization constructions for coherent sheaves on stacks are used to define reduced Gromov-Witten invariants of GIT quotients in higher genera.
A smooth compactification of the space of genus two curves in projective space: via logarithmic geometry and Gorenstein curves
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Higher genus reduced Gromov--Witten invariants via desingularizations of sheaves
Two desingularization constructions for coherent sheaves on stacks are used to define reduced Gromov-Witten invariants of GIT quotients in higher genera.