Abstract : It is well known that plurigenus does not vanish for a sufficiently large multiple on a canonical threefold over ${\mathbb C}$. There is Reid-Fletcher formula for plurigenus. But, unlike in the case of surface of general type, it is not easy to compute plurigenus. In this paper, we induce a different version of Reid-Fletcher formula and show that the constant term in the induced formula has periodic properties. Using these properties we have an application to nonvanishing of plurigenus.
Keywords : pluricanonical system, plurigenus, threefold of general type
