The tangential branch locus B X/Y ⊂ 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… (More)

Let π : X/S → Y/S be a dominant morphism of S-schemes, where Y and S are Nœtherian and X is a Krull scheme, so X and Y are integral. Let dπ : TX/S → TX/S→Y/S be its tangent morphism and ψ : π (TY/S)→… (More)

We study, in the setting of algebraic varieties, finite-dimensional spaces of functions V that are invariant under a ring D V of differential operators, and give conditions under which D V acts… (More)

We consider modules M over Lie algebroids gA which are of finite type over a local noetherian ring A. Using ideals J ⊂ A such that gA ·J ⊂ J and the length lgA(M/JM) < ∞ we can define in a natural… (More)

Although malignant melanomas are often associated with cytotoxic lymphocyte infiltration, these cells are largely ineffective in inducing tumour cell kill, indicating that the melanoma cells have… (More)

To a dominant morphism π : X/S → Y/S of Nœtherian integral S-schemes one has the inclusion Cπ ⊂ Bπ of the critical locus in the branch locus of π. Conditions on the relative differentials ΩX/Y , ΩX/S… (More)