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

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.