Existence of flips and minimal models for 3-folds in char \(p\) (Q2801757)
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scientific article; zbMATH DE number 6571732
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence of flips and minimal models for 3-folds in char \(p\) |
scientific article; zbMATH DE number 6571732 |
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21 April 2016
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minimal models
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flips
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3-folds
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Existence of flips and minimal models for 3-folds in char \(p\) (English)
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Let \((X,B)\) be a \(\mathbb Q\)-factorial pair defined over an algebraically closed field \(k\) of characteristic \(p>5\). In this paper, building on results of \textit{C. D. Hacon} and \textit{C. Xu} [J. Am. Math. Soc. 28, No. 3, 711--744 (2015; Zbl 1326.14032)], the author shows the following fundamental results: if \((X,B)\) is dlt and \(f:X\to Z\) is a flipping contraction, then the flip of \(f\) exists; if \((X,B)\) is klt and \(K_X+B\) is pseudo-effective then \((X,B)\) has a minimal model; if \((X,B)\) is klt and \(K_X+B\) is big then the pluricanonical ring \(R(K_X+B)\) is finitely generated.
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