1. CMB 2017 (vol 61 pp. 201)
 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 

2. CMB 2016 (vol 60 pp. 522)
 Iena, Oleksandr; Leytem, Alain

On the Singular Sheaves in the Fine Simpson Moduli Spaces of $1$dimensional Sheaves
In the Simpson moduli space $M$ of semistable sheaves with
Hilbert polynomial $dm1$ on a projective plane we study the
closed subvariety $M'$ of sheaves that are not locally free on
their support. We show that for $d\ge 4$ it is a singular subvariety
of codimension $2$ in $M$. The blow up of $M$ along $M'$ is interpreted
as a (partial) modification of $M\setminus M'$ by line bundles
(on support).
Keywords:Simpson moduli spaces, coherent sheaves, vector bundles on curves, singular sheaves Category:14D20 

3. CMB 2016 (vol 59 pp. 858)
 Osserman, Brian

Stability of Vector Bundles on Curves and Degenerations
We introduce a weaker notion of (semi)stability for vector bundles
on
reducible curves which does not depend on a choice of polarization,
and
which suffices for many applications of degeneration techniques.
We explore the basic
properties of this alternate notion of (semi)stability. In a
complementary
direction, we record a proof of the existence of semistable extensions
of vector bundles in suitable degenerations.
Keywords:vector bundle, stability, degeneration Categories:14D06, 14H60 

4. CMB 2013 (vol 57 pp. 439)
 Yang, YanHong

The Fixed Point Locus of the Verschiebung on $\mathcal{M}_X(2, 0)$ for Genus2 Curves $X$ in Charateristic $2$
We prove that for every ordinary genus$2$ curve $X$ over a finite
field $\kappa$ of characteristic $2$ with
$\textrm{Aut}(X/\kappa)=\mathbb{Z}/2\mathbb{Z} \times S_3$, there exist
$\textrm{SL}(2,\kappa[\![s]\!])$representations of $\pi_1(X)$ such
that the image of $\pi_1(\overline{X})$ is infinite. This result
produces a family of examples similar to Laszlo's counterexample
to de Jong's question regarding the finiteness of the geometric
monodromy of representations of the fundamental group.
Keywords:vector bundle, Frobenius pullback, representation, etale fundamental group Categories:14H60, 14D05, 14G15 

5. CMB 2004 (vol 47 pp. 624)
 Zhang, Xi

A Compactness Theorem for YangMills Connections
In this paper, we consider YangMills connections
on a vector bundle $E$ over a compact Riemannian manifold $M$ of
dimension $m> 4$, and we show that any set of YangMills
connections with the uniformly bounded $L^{\frac{m}{2}}$norm of
curvature is compact in $C^{\infty}$ topology.
Keywords:YangMills connection, vector bundle, gauge transformation Categories:58E20, 53C21 

6. CMB 2001 (vol 44 pp. 452)
 Ishihara, Hironobu

Some Adjunction Properties of Ample Vector Bundles
Let $\ce$ be an ample vector bundle of rank $r$ on a projective
variety $X$ with only logterminal singularities. We consider the
nefness of adjoint divisors $K_X + (tr) \det \ce$ when $t \ge \dim X$
and $t>r$. As an application, we classify pairs $(X,\ce)$ with
$c_r$sectional genus zero.
Keywords:ample vector bundle, adjunction, sectional genus Categories:14J60, 14C20, 14F05, 14J40 
