Computing isolated orbifolds in weighted flag varieties
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Given a weighted flag variety wΣ(μ,u) corresponding to chosen fixed parameters μ and u, we present an algorithm to compute lists of all possible projectively Gorenstein n-folds, having canonical weight k and isolated orbifold points, appearing as weighted complete intersections in wΣ(μ,u) or some projective cone(s) over wΣ(μ,u). We apply our algorithm to compute lists of interesting classes of polarized 3-folds with isolated orbifold points in the codimension 8 weighted G_2 variety. We also show the existence of some families of log-terminal Q-Fano 3-folds in codimension 8 by explicitly constructing them as quasilinear sections of a weighted G_2-variety.
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