Complex projective threefolds with non-negative canonical Euler-Poincare characteristic

TL;DR

This paper establishes bounds on the pluricanonical maps of complex projective threefolds of general type with non-negative Euler characteristic, proving birationality for sufficiently large multiples of the canonical bundle.

Contribution

It provides explicit birationality bounds for m-canonical maps of such threefolds, confirming the optimality of these bounds with known examples.

Findings

Birationality of $ ext{m-canonical}$ maps for $m extgreater= 14$ (resp. 8)

Optimal bounds confirmed by examples

Advances understanding of pluricanonical maps in algebraic geometry

Abstract

Let $V$ be a complex nonsingular projective 3-fold of general type with $\chi(\omega_V)\geq 0$ (resp. $>0$). We prove that the m-canonical map $\Phi_{|mK_V|}$ is birational onto its image for all $m\ge 14$ (resp. $\geq 8$). Known examples show that the lower bound $r_3=14$ (resp. $=8$) is optimal.