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The Zariski-Lipman conjecture for complete intersections
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences. (Matematik)
2011 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 337, no 1, 169-180 p.Article in journal (Refereed) Published
Abstract [en]

The tangential branch locus BX/Yt∩BX/Y is the subset of points in the branch locus where the sheaf of relative vector fields TX/Y fails to be locally free. It was conjectured by Zariski and Lipman that if V/k is a variety over a field k of characteristic 0 and BV/kt=∅, then V/k is smooth (= regular). We prove this conjecture when V/k is a locally complete intersection. We prove also that BV/kt=∅ implies codimXBV/k≤1 in positive characteristic, if V/k is the fibre of a flat morphism satisfying generic smoothness.

Place, publisher, year, edition, pages
2011. Vol. 337, no 1, 169-180 p.
Keyword [en]
Algebraic geometry; Commutative algebra; Derivations; Smooth morphisms
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hig:diva-9613DOI: 10.1016/j.jalgebra.2011.05.003ISI: 000291288700009ScopusID: 2-s2.0-79956286767OAI: oai:DiVA.org:hig-9613DiVA: diva2:425794
Available from: 2011-06-22 Created: 2011-06-22 Last updated: 2014-11-09Bibliographically approved

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Källström, Rolf
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