Towards a separation theorem of points by adjoint linear systems on polarized threefolds

Abstract

Main Result: Let $(M,L)$ be a smooth complex polarized threefold. Then the linear system $| K+tL|$ separates any two different points on $M$ for any $t\ge 6$, where $K$ is the canonical bundle of $M$. The argument in the proof is a variant of Ein-Lazarsfeld method. Although it is less powerful, it is cheaper, i.e., needs fewer pages. Unfortunately, at present, I cannot show the very ampleness because of technical difficulties. Some related topics are also discussed. A hard copy is available on request to the author.