On generic finiteness of pluricanonical maps of threefolds of general type

Tianyue Zhang

paper

On generic finiteness of pluricanonical maps of threefolds of general type

arXiv:2607.02066

Abstract

We prove that $∣6 K_{X} ∣$ 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 $∣ n K_{X} ∣$ 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.