The Zariski-Lipman conjecture for complete intersections
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
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.
Algebraic geometry; Commutative algebra; Derivations; Smooth morphisms
IdentifiersURN: 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