On a computation of plurigenera of a canonical threefold

For a canonical threefold X, we know for a sufficiently large n. When , there are few known results about the integer n. This paper introduces an algorithm for computing plurigenera. Furthermore, when is small, especially 1 and 2, plurigenera are computed. This produces for n 7 and for n 10 when . Also, for n 14 and for n 20 with 8 possible exceptional cases when .