Non-normal purely log terminal centres in characteristic \(p \geqslant 3\). (English) Zbl 1461.14021
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 [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 [C. Hacon and 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 [P. Cascini and 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 \(p > 3\).
Reviewer: Diletta Martinelli (Amsterdam)
MSC:
| 14E30 | Minimal model program (Mori theory, extremal rays) |
| 14J17 | Singularities of surfaces or higher-dimensional varieties |
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