1. CJM 2007 (vol 59 pp. 1098)
 Rodrigues, B.

Ruled Exceptional Surfaces and the Poles of Motivic Zeta Functions
In this paper we study ruled surfaces which appear as an exceptional
surface in a succession of blowingups. In particular we prove
that the $e$invariant of such a ruled exceptional surface $E$ is
strictly positive whenever its intersection with the other
exceptional surfaces does not contain a fiber (of $E$). This fact
immediately enables us to resolve an open problem concerning an
intersection configuration on such a ruled exceptional surface
consisting of three nonintersecting sections. In the second part
of the paper we apply the nonvanishing of $e$ to the study of the
poles of the wellknown topological, Hodge and motivic zeta
functions.
Categories:14E15, 14J26, 14B05, 14J17, 32S45 

2. CJM 2002 (vol 54 pp. 55)
 Ban, Chunsheng; McEwan, Lee J.; Némethi, András

On the Milnor Fiber of a Quasiordinary Surface Singularity
We verify a generalization of (3.3) from \cite{Le} proving
that the homotopy type of the Milnor fiber of a reduced
hypersurface singularity depends only on the embedded
topological type of the singularity. In particular, using
\cite{Za,Li1,Oh1,Gau} for irreducible quasiordinary germs,
it depends only on the normalized distinguished pairs of the
singularity. The main result of the paper provides an explicit
formula for the Eulercharacteristic of the Milnor fiber in the
surface case.
Categories:14B05, 14E15, 32S55 

3. CJM 2001 (vol 53 pp. 834)
 Veys, Willem

Zeta Functions and `Kontsevich Invariants' on Singular Varieties
Let $X$ be a nonsingular algebraic variety in characteristic zero. To
an effective divisor on $X$ Kontsevich has associated a certain
motivic integral, living in a completion of the Grothendieck ring of
algebraic varieties. He used this invariant to show that birational
(smooth, projective) CalabiYau varieties have the same Hodge
numbers. Then Denef and Loeser introduced the invariant {\it motivic
(Igusa) zeta function}, associated to a regular function on $X$, which
specializes to both the classical $p$adic Igusa zeta function and the
topological zeta function, and also to Kontsevich's invariant.
This paper treats a generalization to singular varieties. Batyrev
already considered such a `Kontsevich invariant' for log terminal
varieties (on the level of Hodge polynomials of varieties instead of
in the Grothendieck ring), and previously we introduced a motivic zeta
function on normal surface germs. Here on any $\bbQ$Gorenstein
variety $X$ we associate a motivic zeta function and a `Kontsevich
invariant' to effective $\bbQ$Cartier divisors on $X$ whose support
contains the singular locus of~$X$.
Keywords:singularity invariant, topological zeta function, motivic zeta function Categories:14B05, 14E15, 32S50, 32S45 

4. CJM 2000 (vol 52 pp. 1018)
 Reichstein, Zinovy; Youssin, Boris

Essential Dimensions of Algebraic Groups and a Resolution Theorem for $G$Varieties
Let $G$ be an algebraic group and let $X$ be a generically free $G$variety.
We show that $X$ can be transformed, by a sequence of blowups with smooth
$G$equivariant centers, into a $G$variety $X'$ with the following
property the stabilizer of every point of $X'$ is isomorphic to a
semidirect product $U \sdp A$ of a unipotent group $U$ and a
diagonalizable group $A$.
As an application of this result, we prove new lower bounds on essential
dimensions of some algebraic groups. We also show that certain
polynomials in one variable cannot be simplified by a Tschirnhaus
transformation.
Categories:14L30, 14E15, 14E05, 12E05, 20G10 
