On the pluricanonical map and the canonical volume of projective 4-folds of general type

TL;DR

This paper establishes new bounds on the birationality of pluricanonical maps and the canonical volume for nonsingular projective 4-folds of general type, improving previous results by Meng Chen.

Contribution

It provides explicit birationality thresholds and a lower bound for the canonical volume of 4-folds, advancing understanding of their geometric properties.

Findings

Birationality of rac{m}{} ext{maps} ext{for} m ext{beyond} 76m_0+77

Lower bound for canonical volume: rac{1}{1680m_0(m_0+1)^3}

Improves previous bounds established by Meng Chen

Abstract

For nonsingular projective 4-folds V of general type with plurigenus $P_{m_0}(V) \geq 2$ for some positive integer $m_0$, we show that $\varphi_{m}$ is birational onto its image for all integers $m \geq 76m_0+77$ and the canonical volume Vol(V) has the lower bound $\frac{1}{1680m_0(m_0+1)^3}$. This improves earlier results of Meng Chen.