On the plurigenus of a canonical threefold

Abstract

It is well known that plurigenus does not vanish for a sufficiently large multiple on a canonical threefold over 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. © 2012 The Korean Mathematical Society.