Much inspired by a joint work with Professors Tien-Cuong Dinh, De-Qi Zhang and Doctor Hsueh-Yung Lin and seminal works by Artin, Van den Bergh and Keeler, I determine the possible Gelfand-Kirillov dimensions of twisted homogeneous coordinate rings arising from projective threefolds and projective hyperkaehler manifolds, in a fairly complete way at least with optimal upper bound. This is a generalization of a result of Artin and Van den Bergh for surfaces and a refinement of a result of Keeler in dimension 3.

(This is a talk of Tokyo-Kyoto AG seminar on Zoom, and will be given in Japanese.)