光滑三重奇异曲线的除法抽取，I
Divisorial Extractions from Singular Curves in Smooth 3-Folds, I
摘要：
考虑包含在光滑3重$X$中的奇异曲线$Γ$。假设一般的大象猜想，一般的超曲面部分$Γ\subset S\subset X$是杜瓦尔。在此假设下，本文描述了构造一个除数提取$Γ$的Kustin-Miller非投影。如果$S$为$D_{2k}, E_7$或$E_8$型，则证明不存在$Γ\subset X$的末端提取物，如果$S$为$A_1,A_2$或$E_6$型，则进行分类。$A_n$和$D_{2k+1}$情况将在另一篇论文中讨论。
英文摘要：
Consider a singular curve $Γ$ contained in a smooth 3-fold $X$. Assuming the general elephant conjecture, the general hypersurface section $Γ\subset S\subset X$ is Du Val. Under that assumption, this paper describes the construction of a divisorial extraction from $Γ$ by Kustin--Miller unprojection. Terminal extractions from $Γ\subset X$ are proved not to exist if $S$ is of type $D_{2k}, E_7$ or $E_8$ and are classified if $S$ is of type $A_1,A_2$ or $E_6$. The $A_n$ and $D_{2k+1}$ cases shall be considered in a further paper.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
