1. CMB Online first
 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 

2. 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 

3. 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 

4. 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 

5. 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 
