Locally nilpotent derivations of affine domains
Any locally nilpotent derivation of an affine domain is equivalent to a restriction of a Jacobian type derivation of a polynomial ring.
On the cancellation problem for surfaces
Abstract In this Note we prove a conjecture formulated by Danielewski. As a consequence we obtain an infinite dimensional family of non-isomorphic surfaces X λ with the property that all X λ × ℂ are isomorphic.
Triangular monomial derivations on k[X1,X2,X3,X4] have kernel generated by at most four elements
Abstract It is shown that any triangular derivation on k [ X 1 , X 2 , X 3 , X 4 ] sending X i to a monomial has kernel generated by at most four elements, hence is finitely generated. An explicit formula for the generators is given.