arXiv subjects
Publications and source records attributed to Jianshi Yan.
We prove that for all nonsingular projective 3-folds of general type with third plurigenus $P_3 \geq 2$, the pluricanonical map $φ_m$ is birational onto its image for all $m \geq 14$, which is optimal.
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 $φ_{m}$ 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.
We answer an open problem of the first author and Zhang (see Open Problem 6.4 (3) in Math. Z. 258 (2008), 565-585) and prove that, for any nonsingular projective $3$-fold of general type with the geometric genus greater than 201, the bicanonical system is not composed of any pencil of surfaces.
We show that, for nonsingular projective 4-folds V of general type with geometric genus $p_g\geq 2$, the 33-canonical map is birational onto the image and the canonical volume has the lower bound $1/520$, which improves a previous theorem by Chen and Chen.