Computing isolated orbifolds in weighted flag varieties. (March 2017) - Qureshi, Muhammad Imran
Abstract: Given a weighted flag variety w Σ ( 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 w Σ ( μ, u ) or some projective cone(s) over w Σ ( 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.