On torsion-freeness of Kähler differential sheaves

2023/06/14 by Das, Nilkantha, Roy, Sumit
#13N05 #14B05 #14F10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.08628

Abstract

Let X be a normal algebraic variety over an algebraically closed field k of characteristic zero. We prove that the Kähler 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×_k X, defined outside the singular locus of X ×_k X, extends regularly to the singular locus.

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