# On the Lipman–Zariski conjecture for logarithmic vector fields on log canonical pairs

@article{Bergner2017OnTL,
title={On the Lipman–Zariski conjecture for logarithmic vector fields on log canonical pairs},
author={Hannah Bergner},
journal={arXiv: Algebraic Geometry},
year={2017}
}
We consider a version of the Lipman-Zariski conjecture for logarithmic vector fields and logarithmic $1$-forms on pairs. Let $(X,D)$ be a pair consisting of a normal complex variety $X$ and an effective Weil divisor $D$ such that the sheaf of logarithmic vector fields (or dually the sheaf of reflexive logarithmic $1$-forms) is locally free. We prove that in this case the following holds: If $(X,D)$ is dlt, then $X$ is necessarily smooth and $\lfloor D\rfloor$ is snc. If $(X,D)$ is lc or the… Expand
1 Citations
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