“…The study of toric varieties whose blowup at a general point is not a Mori dream space has attracted a lot of interest recently (see [GK16], [HKL18], [GK19], [He19], [KN19], [GAGK20]) and often plays a pivotal role in determining whether a given variety is a Mori dream space (e.g. [CT15], [GK16], [HKL18]).…”