Higher rank Brill—Noether theory and coherent systems open questions Page 1 Higher rank
Brill—Noether theory and coherent systems open questions Peter E. Newstead University of …

It is known that on a smooth projective variety, a strongly slope semistable bundle with
vanishing discriminant is nef if and only if its determinant is nef. We generalize this theorem …

We show the kernel sheaf associated to a sufficiently positive torsion-free sheaf of rank one
is slope stable. Furthermore, we are able to give an explicit bound for “sufficiently positive.” …

The notion of linear stability of a variety in projective space was introduced by Mumford in
the context of GIT. It has subsequently been applied by Mistretta and others to Butler's …

There is a well studied notion of GIT-stability for coherent systems over curves, which
depends on a real parameter $\alpha $. For generated coherent systems, there is a further …

Our purpose in this paper is to construct new examples of twisted Brill-Noether loci on
curves of genus $ g\ge2 $. Many of these examples have negative expected dimension. We …

Using techniques from Bridgeland stability, we show the kernel sheaf associated to
sufficiently positive Gieseker stable sheaf on a Del Pezzo surface is slope stable. This is the …

Let $ C $ be a comb-like curve over $\mathbb {C} $, and $ E $ be a vector bundle of rank $ n
$ on $ C $. In this paper, we investigate the criteria for the semistability of the restriction of …

Let X be a non-singular irreducible complex projective curve of genus g≥ 2. The concept of
stability of coherent systems over X depends on a positive real parameter α, given then a …

25 open questions about vector bundles and their moduli SciELO - Scientific Electronic
Library Online vol.41 número2 Curves in projective spaces: questions and remarks Some …