Existence of flips and minimal models for 3-folds in char \(p\)
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.
scientific article; zbMATH DE number 6571732