@article{994205e688304a32badd88155804724e,
title = "(Co)torsion of exterior powers of differentials over complete intersections",
abstract = "The main goal of this paper is to establish a generalized Lipman-Zariski result in characteristic zero for complete intersection germs whose singular locus has codimension at least three, generalizing the corresponding result of Graf for hypersurfaces. More precisely, we prove that the condition that the sheaf of reflexive K{\"a}hler differential p-forms is free implies smoothness. The proof given here rests on recognizing the torsion, as was known previously, and the cotorsion as homologies of the generalized Koszul complexes constructed by Kirby, Buchsbaum-Eisenbud, Lebelt, and Bruns-Vetter and applying certain rigidity and symmetry results based on work of Lebelt and Rodicio, yielding also a different proof of Graf{\textquoteright}s result. To make the paper accessible to both complex analysts and algebraic geometers we include full descriptions of the necessary background.",
keywords = "Differentials, Homology groups, Resolution, Singularity, Torsion",
author = "Claudia Miller and Sophia Vassiliadou",
note = "Funding Information: This paper began in the summer of 2014 while the authors were visiting the Department of Mathematics at the University of Nebraska, Lincoln. Both authors would like to thank Pro-fessors Avramov, Walker, Iyengar for lending an ear and the Department of Mathematics at the University of Nebraska for logistical support. The project reached a critical stage while the second author was on leave from Georgetown University in 2016-2017. She would like to thank the Department of Mathematics at the University of Maryland in College Park for letting her use an office there during that time, Professor Jim Schaffer for a stimulating course in Homological Algebra in the fall of 2016 and Tom Haines for many fruitful discussions and constant support. The authors are indebted to the referee for his or her critical reading of the manuscript, point-ing out inaccuracies or inconsistencies, suggesting ways to clarify or correct certain statements in the paper, and making the paper easier to read. Publisher Copyright: {\textcopyright} 2019, Worldwide Center of Mathematics. All rights reserved.",
year = "2019",
doi = "10.5427/jsing.2019.19h",
language = "English (US)",
volume = "19",
pages = "131--162",
journal = "Journal of Singularities",
issn = "1949-2006",
publisher = "Worldwide Center of Mathematics",
}