#### 130 Citations

ACTA MATHEMATICA VIETNAMICA

- 2011

Let f : R → R be a polynomial of degree d with only isolated complex critical points. It is shown that the set of bifurcation values of f is contained in a set which has at most (d − 1) points. The… Expand

Unipotent group actions on affine varieties

- Mathematics, Engineering
- 2010

Abstract Algebraic actions of unipotent groups U on affine k-varieties X (k is an algebraically closed field of characteristic 0) for which the algebraic quotient X / / U has small dimension are… Expand

Derivations of polynomial rings over a field of characteristic zero

- 2013

This set is a k-subalgebra of A which we call the ring of constants of d. If A is a domain and k is a field, then we denote by A0 the field of quotients of A and we denote also by d the unique… Expand

Counterexamples to the Fourteenth Problem of

- 2005

Let K be a field, K[X] = K[X1, . . . , Xn] the polynomial ring in n variables over K for some n ∈ N, and K(X) the field of fractions of K[X]. Assume that L is a subfield of K(X) containing K. Then,… Expand

The fourteenth problem of Hilbert for polynomial derivations

- Mathematics
- 2002

We present some facts, observations and remarks concerning the problem of finiteness of the rings of constants for derivations of polynomial rings over a commutative ring k containing the field Q of… Expand

Counterexample to Hilbert''s fourteenth problem for three dimensional additive groups

- Mathematics
- 2001

A CHARACTERIZATION OF LINEARLY REDUCTIVEGROUPS BY THEIR INVARIANTSG

- 2000

The theorem of Hochster and Roberts says that, for every module V of a linearly reductive group G over a eld K, the invariant ring KV ] G is Cohen{Macaulay. We prove the following converse: if G is a… Expand

The Positivity of Intersection Multiplicities and Symbolic Powers of Prime Ideals

- Mathematics
- Compositio Mathematica
- 2000

Serre's nonnegativity conjecture for intersection multiplicities has recently been proven by O. Gabber. In this paper we investigate Serre's positivity conjecture using the methods which he… Expand

Invariants of Hopf Algebras

- Mathematics
- 1999

In the winter of 1999 I gave a series of lectures at Queen’s university about some recent results concerning the Cohen-Macaulay property of invariants of Hopf algebras. Tony Geramita asked me to… Expand

Commutative Ring Theory

- Mathematics
- 1989

Preface Introduction Conventions and terminology 1. Commutative rings and modules 2. prime ideals 3. Properties of extension rings 4. Valuation rings 5. Dimension theory 6. Regular sequences 7.… Expand