Two desingularization constructions for coherent sheaves on stacks are used to define reduced Gromov-Witten invariants of GIT quotients in higher genera.
A desingularization of the main component of the moduli space of genus-one stable maps into P^n
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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.