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The Zariski-Lipman conjecture for log canonical spaces. (English) Zbl 1357.14009
In the paper under the review, the author proves a special case of the Zariski-Lipman conjecture (which asserts that a complex variety $$X$$ with a locally free tangent sheaf $$T_X$$ is necessarily smooth). His main result states as follows: let $$X$$ be a log canonical space such that the tangent sheaf $$T_X$$ is locally free, then $$X$$ is smooth. The log canonical spaces are related to the minimal model programm. Let us mention that the author obtain his main result by proving the following more general theorem: let $$(X,B)$$ be a log canonical pair such that the tangent sheaf $$T_X$$ is locally free, then $$X$$ is smooth.

##### MSC:
 14B05 Singularities in algebraic geometry 32B05 Analytic algebras and generalizations, preparation theorems 32S65 Singularities of holomorphic vector fields and foliations
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