On generic finiteness of pluricanonical maps of threefolds of general type

Abstract

We prove that $|6K_X|$ defines a generically finite map for all minimal 3-folds $X$ of general type with $P_2(X)\geq 2$, which is optimal. We also prove that $|nK_X|$ defines a generically finite map for all minimal 3-folds $X$ of general type when $n\geq 38$. The essential technical ingredients of this paper are a new generic finiteness criterion for surfaces and an effective comparison inequality under a special resolution.