The Zariski-Lipman conjecture for complete intersections

JOURNAL OF ALGEBRA

卷:337

Article

Kallstrom, Rolf

关键词: Smooth morphisms;    Commutative algebra;    Algebraic geometry;    Derivations;   

DOI  :  10.1016/j.jalgebra.2011.05.003

来源: Elsevier

【 摘 要 】

The tangential branch locus B-X/Y(t) subset of B-X/Y is the subset of points in the branch locus where the sheaf of relative vector fields T-X/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 B-V/k(t) = empty set. then V/k is smooth (= regular). We prove this conjecture when V/k is a locally complete intersection. We prove also that B-V/K(t) = empty set implies codim(X) B-V/K <= 1 in positive characteristic, if V/k is the fibre of a flat morphism satisfying generic smoothness. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free