arXiv 2201.066462022-01math.AGmath.AC

The Violation of the Lipman-Zariski conjecture in positive characteristic

Patrick Graf

备注：: Final version
发表信息：: J. Algebra 601 (2022), pp. 115-128
DOI：: 10.1016/j.jalgebra.2022.03.004

英文摘要：

We study the failure of the Lipman-Zariski conjecture in positive characteristic. For rational double points, the conjecture holds true except for a short finite list of exceptions. For log canonical surface singularities, the conjecture continues to hold with the same list of exceptions under an additional tameness hypothesis. In particular, among rational double points in characteristic $p \ge 7$ Lipman's counterexample is the only one, and the conjecture holds for all tame $F$-pure normal surface singularities.

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