1. CMB Online first
 Fiori, Andrew

A RiemannHurwitz Theorem for the Algebraic Euler Characteristic
We prove an analogue of the RiemannHurwitz theorem for computing
Euler characteristics of pullbacks of coherent sheaves through
finite maps of smooth projective varieties in arbitrary dimensions,
subject only to the condition that the irreducible components
of the branch and ramification locus have simple normal crossings.
Keywords:RiemannHurwitz, logarithmicChern class, Euler characteristic Categories:14F05, 14C17 

2. CMB 2014 (vol 57 pp. 658)
 Thang, Nguyen Tat

Admissibility of Local Systems for some Classes of Line Arrangements
Let $\mathcal{A}$ be a line arrangement in the complex
projective plane $\mathbb{P}^2$ and let $M$ be its complement. A rank one
local system $\mathcal{L}$ on $M$ is admissible if roughly speaking
the cohomology groups
$H^m(M,\mathcal{L})$ can be computed directly from the cohomology
algebra $H^{*}(M,\mathbb{C})$. In this work, we give a sufficient
condition for the admissibility of all rank one local systems on
$M$. As a result, we obtain some properties of the characteristic
variety $\mathcal{V}_1(M)$ and the Resonance variety $\mathcal{R}_1(M)$.
Keywords:admissible local system, line arrangement, characteristic variety, multinet, resonance variety Categories:14F99, 32S22, 52C35, 05A18, 05C40, 14H50 

3. CMB 2011 (vol 55 pp. 368)
 Nie, Zhaohu

The Secondary ChernEuler Class for a General Submanifold
We define and study the secondary ChernEuler class for a general submanifold of a Riemannian manifold. Using this class, we define and study the index for a vector field with nonisolated singularities on a submanifold. As an application, we give conceptual proofs of a result of Chern.
Keywords:secondary ChernEuler class, normal sphere bundle, Euler characteristic, index, nonisolated singularities, blowup Category:57R20 

4. CMB 2011 (vol 55 pp. 164)
 Pergher, Pedro L. Q.

Involutions Fixing $F^n \cup \{\text{Indecomposable}\}$
Let $M^m$ be an $m$dimensional, closed and smooth manifold, equipped with a smooth involution $T\colon M^m \to M^m$ whose fixed point set has the form $F^n \cup F^j$, where $F^n$ and $F^j$ are submanifolds with dimensions $n$ and $j$, $F^j$ is indecomposable and $ n >j$. Write $nj=2^pq$, where $q \ge 1$ is odd and $p \geq 0$, and set $m(nj) = 2n+pq+1$ if $p \leq q + 1$
and $m(nj)= 2n + 2^{pq}$ if $p \geq q$. In this paper we show that $m \le m(nj) + 2j+1$. Further, we show that this bound is \emph{almost} best possible, by exhibiting examples $(M^{m(nj) +2j},T)$ where the fixed point set of
$T$ has the form $F^n \cup F^j$ described above, for every $2 \le j
Keywords:involution, projective space bundle, indecomposable manifold, splitting principle, StiefelWhitney class, characteristic number Category:57R85 

5. CMB 2010 (vol 54 pp. 56)
 Dinh, Thi Anh Thu

Characteristic Varieties for a Class of Line Arrangements
Let $\mathcal{A}$ be a line arrangement in the complex projective plane
$\mathbb{P}^2$, having the points of multiplicity $\geq 3$ situated on two
lines in $\mathcal{A}$, say $H_0$ and $H_{\infty}$. Then we show that the
nonlocal irreducible components of the first resonance variety
$\mathcal{R}_1(\mathcal{A})$ are 2dimensional and correspond to parallelograms $\mathcal{P}$ in
$\mathbb{C}^2=\mathbb{P}^2 \setminus H_{\infty}$ whose sides are in $\mathcal{A}$ and for
which $H_0$ is a diagonal.
Keywords:local system, line arrangement, characteristic variety, resonance variety Categories:14C21, 14F99, 32S22, 14E05, 14H50 

6. CMB 2004 (vol 47 pp. 22)
 Goto, Yasuhiro

A Note on the Height of the Formal Brauer Group of a $K3$ Surface
Using weighted Delsarte surfaces, we give examples of $K3$ surfaces
in positive characteristic whose formal Brauer groups have height
equal to $5$, $8$ or $9$. These are among the four values of the
height left open in the article of Yui \cite{Y}.
Keywords:formal Brauer groups, $K3$ surfaces in positive, characteristic, weighted Delsarte surfaces Categories:14L05, 14J28 
