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On torsion-freeness of K\'{a}hler differential sheaves
- Publication Year :
- 2023
-
Abstract
- 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.<br />Comment: 7 pages. Comments are welcome
- Subjects :
- Mathematics - Algebraic Geometry
14F10, 13N05, 14B05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2306.08628
- Document Type :
- Working Paper