On a computation of plurigenera of a canonical threefold

For a canonical threefold X, we know h0(X,OX(nKX))⩾1 for a sufficiently large n. When χ(OX)>0, there are few known results about the integer n. This paper introduces an algorithm for computing plurigenera. Furthermore, when χ(OX) is small, especially 1 and 2, plurigenera are computed. This produces h0(X,OX(nKX))⩾1 for n⩾7 and h0(X,OX(nKX))⩾2 for n⩾10 when χ(OX)=1. Also, h0(X,OX(nKX))⩾1 for n⩾14 and h0(X,OX(nKX))⩾2 for n⩾20 with 8 possible exceptional cases when χ(OX)=2.