1. CMB Online first
 Reichstein, Zinovy B.

On a property of real plane curves of even degree
F. Cukierman asked whether or not for every
smooth
real plane curve $X \subset \mathbb{P}^2$ of even degree $d \geqslant
2$
there exists a real line
$L \subset \mathbb{P}^2$ such $X \cap L$ has no real points.
We show that the answer is ``yes" if $d = 2$ or $4$ and ``no"
if $n \geqslant 6$.
Keywords:real algebraic geometry, plane curve, maximizer function, bitangent Categories:14P05, 14H50 

2. CMB Online first
 Shirane, Taketo

Connected numbers and the embedded topology of plane curves
The splitting number of a plane irreducible curve for a Galois
cover is effective to distinguish the embedded topology of plane
curves.
In this paper, we define the connected number of a plane
curve (possibly reducible) for a Galois cover, which is similar
to the splitting number.
By using the connected number, we distinguish the embedded topology
of Artal arrangements of degree $b\geq 4$, where an Artal arrangement
of degree $b$ is a plane curve consisting of one smooth curve
of degree $b$ and three of its total inflectional tangen
Keywords:plane curve, splitting curve, Zariski pair, cyclic cover, splitting number Categories:14H30, 14H50, 14F45 

3. CMB Online first
 Jeong, Imsoon; de Dios Pérez, Juan; Suh, Young Jin; Woo, Changhwa

Lie derivatives and Ricci tensor on real hypersurfaces in complex twoplane Grassmannians
On a real hypersurface $M$ in a complex twoplane Grassmannian
$G_2({\mathbb C}^{m+2})$ we have the Lie derivation ${\mathcal
L}$ and a differential operator of order one associated to the
generalized TanakaWebster connection $\widehat {\mathcal L}
^{(k)}$. We give a classification of real hypersurfaces $M$ on
$G_2({\mathbb C}^{m+2})$ satisfying
$\widehat {\mathcal L} ^{(k)}_{\xi}S={\mathcal L}_{\xi}S$, where
$\xi$ is the Reeb vector field on $M$ and $S$ the Ricci tensor
of $M$.
Keywords:real hypersurface, complex twoplane Grassmannian, Hopf hypersurface, shape operator, Ricci tensor, Lie derivation Categories:53C40, 53C15 

4. CMB Online first
 Takahashi, Tomokuni

Projective plane bundles over an elliptic curve
We calculate the dimension of cohomology groups for
the holomorphic tangent bundles of each isomorphism
class of the projective plane bundle over an elliptic curve.
As an application, we construct the families
of projective plane bundles, and prove that the families
are effectively parametrized and complete.
Keywords:projective plane bundle, vector bundle, elliptic curve, deformation, KodairaSpencer map Categories:14J10, 14J30, 14D15 

5. CMB 2016 (vol 59 pp. 721)
 Pérez, Juan de Dios; Lee, Hyunjin; Suh, Young Jin; Woo, Changhwa

Real Hypersurfaces in Complex Twoplane Grassmannians with Reeb Parallel Ricci Tensor in the GTW Connection
There are several kinds of classification problems for real hypersurfaces
in complex twoplane Grassmannians $G_2({\mathbb C}^{m+2})$.
Among them, Suh classified Hopf hypersurfaces $M$ in $G_2({\mathbb
C}^{m+2})$ with Reeb parallel Ricci tensor in LeviCivita connection.
In this paper, we introduce the notion of generalized TanakaWebster
(in shortly, GTW) Reeb parallel Ricci tensor for Hopf hypersurface
$M$ in $G_2({\mathbb C}^{m+2})$. Next, we give a complete classification
of Hopf hypersurfaces in $G_2({\mathbb C}^{m+2})$ with GTW Reeb
parallel Ricci tensor.
Keywords:Complex twoplane Grassmannian, real hypersurface, Hopf hypersurface, generalized TanakaWebster connection, parallelism, Reeb parallelism, Ricci tensor Categories:53C40, 53C15 

6. CMB 2016 (vol 59 pp. 449)
 Abdallah, Nancy

On Hodge Theory of Singular Plane Curves
The dimensions of the graded quotients of the
cohomology of a plane curve complement $U=\mathbb P^2 \setminus C$
with respect to the Hodge filtration are described in terms of
simple geometrical invariants. The case of curves with ordinary
singularities is discussed in detail. We also give a precise
numerical estimate for the difference between the Hodge filtration
and the pole order filtration on $H^2(U,\mathbb C)$.
Keywords:plane curves, Hodge and pole order filtrations Categories:32S35, 32S22, 14H50 

7. CMB 2015 (vol 58 pp. 835)
8. CMB 2015 (vol 58 pp. 459)
 Casini, Emanuele; Miglierina, Enrico; Piasecki, Lukasz

Hyperplanes in the Space of Convergent Sequences and Preduals of $\ell_1$
The main aim of the present paper is to investigate various structural
properties
of hyperplanes of $c$, the Banach space of the convergent sequences.
In particular, we give an explicit formula for the projection
constants and we prove that an hyperplane of $c$ is isometric
to the whole space if and only if it is $1$complemented. Moreover,
we obtain the classification
of those hyperplanes for which their duals are isometric to
$\ell_{1}$ and we give a complete description of the preduals
of $\ell_{1}$ under the assumption that the standard basis of
$\ell_{1}$
is weak$^{*}$convergent.
Keywords:space of convergent sequences, projection, $\ell_1$predual, hyperplane Categories:46B45, 46B04 

9. CMB 2014 (vol 57 pp. 697)
10. CMB 2013 (vol 57 pp. 72)
 Grari, A.

Un Anneau Commutatif associÃ© Ã un design symÃ©trique
Dans les articles \cite{1}, \cite{2} et \cite{3}; l'auteur dÃ©veloppe une reprÃ©sentation
d'un plan projectif fini par un
anneau commutatif unitaire dont les propriÃ©tÃ©s algÃ©briques dÃ©pendent
de la structure gÃ©omÃ©trique du plan. Dans l'article \cite{4}; il Ã©tend cette reprÃ©sentation aux designs symÃ©triques. Cependant l'auteur de l'article \cite{7} fait remarquer que la multiplication dÃ©finie dans ce cas ne peut Ãªtre associative que si le design est un plan projectif.
Dans ce papier on mÃ¨nera
une Ã©tude de cette reprÃ©sentation dans le cas des designs
symÃ©triques. On y montrera comment on peut faire associer un
anneau commutatif unitaire Ã
tout design symÃ©trique , on y prÃ©cisera certaines de ses propriÃ©tÃ©s, en
particulier, celles qui relÃ¨vent de son invariance. On caractÃ©risera aussi les gÃ©omÃ©tries projectives finies de dimension supÃ©rieure moyennant cette reprÃ©sentation.
Keywords:projective planes, symmetric designs, commutative rings Categories:05B05, 16S99 

11. CMB 2013 (vol 57 pp. 821)
 Jeong, Imsoon; Kim, Seonhui; Suh, Young Jin

Real Hypersurfaces in Complex TwoPlane Grassmannians with Reeb Parallel Structure Jacobi Operator
In this paper we give a characterization of a real hypersurface of
Type~$(A)$ in complex twoplane Grassmannians ${ { {G_2({\mathbb
C}^{m+2})} } }$, which means a
tube over a totally geodesic $G_{2}(\mathbb C^{m+1})$ in
${G_2({\mathbb C}^{m+2})}$, by
the Reeb parallel structure Jacobi operator ${\nabla}_{\xi}R_{\xi}=0$.
Keywords:real hypersurfaces, complex twoplane Grassmannians, Hopf hypersurface, Reeb parallel, structure Jacobi operator Categories:53C40, 53C15 

12. CMB 2011 (vol 56 pp. 593)
13. CMB 2011 (vol 55 pp. 767)
 Martini, Horst; Wu, Senlin

On Zindler Curves in Normed Planes
We extend the notion of Zindler curve from the Euclidean plane to
normed planes. A characterization of Zindler curves for general
normed planes is given, and the relation between Zindler curves and
curves of constant areahalving distances in such planes is
discussed.
Keywords:rc length, areahalving distance, Birkhoff orthogonality, convex curve, halving pair, halving distance, isosceles orthogonality, midpoint curve, Minkowski plane, normed plane, Zindler curve Categories:52A21, 52A10, 46C15 

14. CMB 2010 (vol 53 pp. 629)
15. CMB 2009 (vol 52 pp. 424)
 Martini, Horst; Spirova, Margarita

Covering Discs in Minkowski Planes
We investigate the following version of the circle covering
problem in strictly convex (normed or) Minkowski planes: to cover
a circle of largest possible diameter by $k$ unit circles. In
particular, we study the cases $k=3$, $k=4$, and $k=7$. For $k=3$
and $k=4$, the diameters under consideration are described in
terms of sidelengths and circumradii of certain inscribed regular
triangles or quadrangles. This yields also simple explanations of
geometric meanings that the corresponding homothety ratios have.
It turns out that basic notions from Minkowski geometry play an
essential role in our proofs, namely Minkowskian bisectors,
$d$segments, and the monotonicity lemma.
Keywords:affine regular polygon, bisector, circle covering problem, circumradius, $d$segment, Minkowski plane, (strictly convex) normed plane Categories:46B20, 52A21, 52C15 

16. CMB 2005 (vol 48 pp. 523)
 Düvelmeyer, Nico

Angle Measures and Bisectors in Minkowski Planes
\begin{abstract}
We prove that a Minkowski plane is Euclidean if and only if Busemann's or
Glogovskij's definitions
of angular bisectors coincide
with a bisector defined by an angular measure in the sense of Brass.
In addition, bisectors defined by the area measure coincide with bisectors
defined by the circumference (arc length) measure
if and only if the unit circle is an
equiframed curve.
Keywords:Radon curves, Minkowski geometry, Minkowski planes,, angular bisector, angular measure, equiframed curves Categories:52A10, 52A21 
