1. 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 

2. 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 

3. 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 

4. 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 

5. 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 
