Non-normal purely log terminal centres in characteristic \(p \geqslant 3\)
The Minimal Model Program (MMP) is an important tool in the classification of higher dimensional algebraic varieties. In complete generality the MMP is still a conjecture but after the breakthrough result in [\textit{C. Birkar} et al., J. Am. Math. Soc. 23, No. 2, 405--468 (2010; Zbl 1210.14019)] the situation in characteristic zero is well understood. Over a field of characteristic \(p > 0\) instead, there are very few known results, in particular existence of flips is still an open conjecture. In [\textit{C. Hacon} and \textit{C. Xu}, J. Am. Math. Soc. 28, No. 3, 711--744 (2015; Zbl 1326.14032)] the authors were able to show that plt centers for threefolds are normal over algebraically closed fields of characteristic \(p > 5\). This allowed them to prove existence of pl-flips in that case. Unfortunately normality of plt centers does not holds in general: the first counterexample was found in [\textit{P. Cascini} and \textit{H. Tanaka}, Am. J. Math. 141, No. 4, 941--979 (2019; Zbl 1460.14040)] in characteristic two. In the paper under review, the author constructs new examples of non-normal plt centers for every prime \(p > 3\).
scientific article; zbMATH DE number 7137472
scientific article