| 吴侃.一般型三维簇的三典范映射[J].数学年刊A辑,2019,(1):001~14 |
| 一般型三维簇的三典范映射 |
| The Third Pluricanonical Map of Threefolds of General Type |
| Received:March 27, 2018 Revised:July 11, 2018 |
| DOI：10.16205/j.cnki.cama.2019.0001 |
| 中文关键词: $3$-Folds of general type, Pluricanonical map, Degree, Fiber type |
| 英文关键词:$3$-Folds of general type, Pluricanonical map, Degree, Fiber type |
| 基金项目: |
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| 中文摘要: |
| 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$p_{g}\geq2$时,
整数$m\geq4$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$\varphi_{3}$不是双有理的, 本文证明了$\varphi_{3}$的映射次数
(如果$\varphi_{3}$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$\varphi_{3}$是纤维型)有一个上界. |
| 英文摘要: |
| 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. |
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