On the pluricanonical map of projective 3-folds of general type with $P_3 \geq 2$

TL;DR

This paper proves that for nonsingular projective 3-folds of general type with third plurigenus at least 2, the pluricanonical map becomes birational onto its image for all m ≥ 14, establishing an optimal bound.

Contribution

It establishes the minimal m for which the pluricanonical map is birational for a class of 3-folds, refining previous bounds.

Findings

Pluricanonical map is birational for all m ≥ 14

Optimal bound for birationality established

Applicable to 3-folds with P_3 ≥ 2

Abstract

We prove that for all nonsingular projective 3-folds of general type with third plurigenus $P_3 \geq 2$, the pluricanonical map $\varphi_m$ is birational onto its image for all $m \geq 14$, which is optimal.