1. CJM Online first
2. CJM 2010 (vol 62 pp. 787)
 Landquist, E.; Rozenhart, P.; Scheidler, R.; Webster, J.; Wu, Q.

An Explicit Treatment of Cubic Function Fields with Applications
We give an explicit treatment of cubic function fields of characteristic at least five. This includes an efficient technique for converting such a field into standard form, formulae for the field discriminant and the genus, simple necessary and sufficient criteria for nonsingularity of the defining curve, and a characterization of all triangular integral bases. Our main result is a description of the signature of any rational place in a cubic extension that involves only the defining curve and the order of the base field. All these quantities only require simple polynomial arithmetic as well as a few squarefree polynomial factorizations and, in some cases, square and cube root extraction modulo an irreducible polynomial. We also illustrate why and how signature computation plays an important role in computing the class number of the function field. This in turn has applications to the study of zeros of zeta functions of function fields.
Keywords:cubic function field, discriminant, nonsingularity, integral basis, genus, signature of a place, class number Categories:14H05, 11R58, 14H45, 11G20, 11G30, 11R16, 11R29 

3. CJM 2008 (vol 60 pp. 572)
 Hitrik, Michael; Sj{östrand, Johannes

NonSelfadjoint Perturbations of Selfadjoint Operators in Two Dimensions IIIa. One Branching Point
This is the third in a series of works devoted to spectral
asymptotics for nonselfadjoint
perturbations of selfadjoint $h$pseudodifferential operators in dimension 2, having a
periodic classical flow. Assuming that the strength $\epsilon$
of the perturbation is in the range $h^2\ll \epsilon \ll h^{1/2}$
(and may sometimes reach even smaller values), we
get an asymptotic description of the eigenvalues in rectangles
$[1/C,1/C]+i\epsilon [F_01/C,F_0+1/C]$, $C\gg 1$, when $\epsilon F_0$ is a saddle point
value of the flow average of the leading perturbation.
Keywords:nonselfadjoint, eigenvalue, periodic flow, branching singularity Categories:31C10, 35P20, 35Q40, 37J35, 37J45, 53D22, 58J40 

4. CJM 2008 (vol 60 pp. 379)
 rgensen, Peter J\o

Finite CohenMacaulay Type and Smooth NonCommutative Schemes
A commutative local CohenMacaulay ring $R$ of finite CohenMacaulay type is known to be an isolated
singularity; that is, $\Spec(R) \setminus \{ \mathfrak {m} \}$ is smooth.
This paper proves a noncommutative analogue. Namely, if $A$ is a
(noncommutative) graded ArtinSchelter \CM\ algebra which is fully
bounded Noetherian and
has finite CohenMacaulay type, then the noncommutative projective scheme determined by
$A$ is smooth.
Keywords:ArtinSchelter CohenMacaulay algebra, ArtinSchelter Gorenstein algebra, Auslander's theorem on finite CohenMacaulay type, CohenMacaulay ring, fully bounded Noetherian algebra, isolated singularity, maximal CohenMacaulay module, noncommutative Categories:14A22, 16E65, 16W50 

5. 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 

6. CJM 2000 (vol 52 pp. 1149)
 Ban, Chunsheng; McEwan, Lee J.

Canonical Resolution of a Quasiordinary Surface Singularity
We describe the embedded resolution of an irreducible quasiordinary
surface singularity $(V,p)$ which results from applying the canonical
resolution of BierstoneMilman to $(V,p)$. We show that this process
depends solely on the characteristic pairs of $(V,p)$, as predicted
by Lipman. We describe the process explicitly enough that a resolution
graph for $f$ could in principle be obtained by computer using only
the characteristic pairs.
Keywords:canonical resolution, quasiordinary singularity Categories:14B05, 14J17, 32S05, 32S25 
