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arXiv · 1403.7614

Divisorial Extractions from Singular Curves in Smooth 3-Folds, I

Tom Ducat
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Abstract

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.

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Tom Ducat. 2014-03-29. Divisorial Extractions from Singular Curves in Smooth 3-Folds, I. https://doi.org/10.1142/s0129167x16500051

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