1. 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 

2. 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 

3. CMB 2007 (vol 50 pp. 427)
 Mejía, Israel Moreno

On the Image of Certain Extension Maps.~I
Let $X$ be a smooth complex projective curve of genus $g\geq
1$. Let $\xi\in J^1(X)$ be a line bundle on $X$ of degree $1$. Let
$W=\Ext^1(\xi^n,\xi^{1})$ be the space of extensions of $\xi^n$
by $\xi^{1}$. There is a rational map
$D_{\xi}\colon G(n,W)\rightarrow SU_{X}(n+1)$,
where $G(n,W)$ is the Grassmannian variety of $n$linear subspaces
of $W$ and $\SU_{X}(n+1)$ is the moduli space of rank $n+1$ semistable
vector
bundles on $X$ with trivial determinant. We prove that if $n=2$,
then $D_{\xi}$ is
everywhere defined and is injective.
Categories:14H60, 14F05, 14D20 

4. CMB 2000 (vol 43 pp. 129)
 Ballico, E.

Maximal Subbundles of Rank 2 Vector Bundles on Projective Curves
Let $E$ be a stable rank 2 vector bundle on a smooth projective
curve $X$ and $V(E)$ be the set of all rank~1 subbundles of $E$
with maximal degree. Here we study the varieties (nonemptyness,
irreducibility and dimension) of all rank~2 stable vector bundles,
$E$, on $X$ with fixed $\deg(E)$ and $\deg(L)$, $L \in V(E)$ and
such that $\card \bigl( V(E) \bigr) \geq 2$ (resp. $\card \bigl(
V(E) \bigr) = 2$).
Category:14H60 

5. CMB 2000 (vol 43 pp. 174)