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On torsion-freeness of K\"{a}hler differential sheaves
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On torsion-freeness of K\"{a}hler differential sheaves
classification
math.AG
keywords
differentialhlerlocussheafsingulartimesalgebraicalgebraically
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Let $X$ be a normal algebraic variety over an algebraically closed field $k$ of characteristic zero. We prove that the K\"{a}hler differential sheaf of $X$ is torsion-free if and only if any regular section of the ideal sheaf of the first order deformation of $X$ inside $X\times_k X$, defined outside the singular locus of $X \times_k X$, extends regularly to the singular locus.
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