一般型三维簇的三典范映射

研究了一般型三维射影代数簇的三典范映射性质.当几何亏格p_g≥2时,整数m≥4的多典范映射结构已经比较清晰,但是三典范映射的结构还有很多未知问题.如果三典范映射φ_3不是双有理的,本文证明了φ_3的映射次数(如果φ_3是一般有限映射)或者一般纤维中一般不可约分支的几何亏格(如果φ_3是纤维型)有一个上界.

The Third Pluricanonical Map of Threefolds of General Type

This paper deals with the third pluricanonical map of $3$-folds of general type. If the geometric genus $p_{g}\geq2$, the structure of the $m$-canonical maps for any integer $m\geq4$ is very clear. But there are many unknown questions for the third pluricanonical map. If the third pluricanonical map $\varphi_{3}$ is not birational, it''s proved that the degree of $\varphi_{3}$ (if $\varphi_{3}$ is generically finite) or the geometric genus of the irreducible component of a general fiber (if $\varphi_{3}$ is of fiber type) is bounded.