Let X be a compact symplectic orbifold groupoid with S being a compact symplectic sub-orbifold groupoid, and X a be the weight-a blowup of X along S with Z being the exceptional divisor. We show that there is a weighted-blowup correspondence between some certain absolute orbifold Gromov-Witten invariants of X relative to S and some certain relative orbifold Gromov-Witten invariants of the pair (X a |Z). As an application, we prove that the symplectic uniruledness of symplectic orbifold groupoids is a weighted-blowup invariant.
In this paper we construct two groupoids from morphisms of groupoids, with one from a categorical viewpoint and the other from a geometric viewpoint. We show that for each pair of groupoids, the two kinds of groupoids of morphisms are equivalent. Then we study the automorphism groupoid of a groupoid.
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