On Kodaira energy and adjoint reduction of polarized threefolds

Abstract

Here we study and classify polarized threefolds whose Kodaira energies are less than -1/2. The Kodaira energy of a polarized manifold (M, L), a pair consisting of a smooth complex algebraic variety M and an ample line bundle L on it, is defined to be $-\Inf{t\in Q\vert κ(K+tL)\ge0}$, where K is the canonical bundle of M and $κ$ denotes the Iitaka dimension of a Q-bundle. The method is a variant of those in my paper; manuscripta math. 76(1992).