Anticanonical system of Fano fivefolds

Abstract

We show that any Fano fivefold with canonical Gorenstein singularities has an effective anticanonical divisor. Moreover,if a general element of the anticanonical system is reduced, then it has canonical singularities. We also prove nonvanishing of anticanonical system in the case of log canonical Gorenstein singularities.

6 pages, final version, to appear in Mathematische Nachrichten, added theorem concerning nonvanishing in case of log canonical Gorenstein Fano fivefold