P. E. Newstead
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View article: New examples of twisted Brill-Noether loci I
New examples of twisted Brill-Noether loci I Open
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 deduce also the existence of a new region in the Brill-Noether map…
View article: Higher rank Brill—Noether theory and coherent systems open questions
Higher rank Brill—Noether theory and coherent systems open questions Open
This article presents a list of open questions on higher rank Brill-Noether theory and coherent systems. Background material and appropriate references are included.
View article: Higher rank Brill-Noether theory and coherent systems: Open questions
Higher rank Brill-Noether theory and coherent systems: Open questions Open
This article presents a list of open questions on higher rank Brill-Noether theory and coherent systems. Background material and appropriate references are included.
View article: Coherent systems on the projective line
Coherent systems on the projective line Open
It is well known that there are no stable bundles of rank greater than 1 on the projective line. In this paper, our main purpose is to study the existence problem for stable coherent systems on the projective line when the number of sectio…
View article: Stability and deformations of generalised Picard sheaves
Stability and deformations of generalised Picard sheaves Open
Let $C$ be a smooth irreducible complex projective curve of genus $g \geq 2$ and $M$ the moduli space of stable vector bundles on $C$ of rank $n$ and degree $d$ with $\gcd(n,d)=1$. A generalised Picard sheaf is the direct image on $M$ of t…
View article: Stability of generalised Picard sheaves
Stability of generalised Picard sheaves Open
Let $C$ be a smooth irreducible complex projective curve of genus $g \geq 2$ and $M_1$ a moduli space of stable vector bundles over $C$. A (generalised) Picard sheaf is the direct image on $M_1$ of the tensor product of the Poincare or uni…
View article: On generated coherent systems and a conjecture of D. C. Butler
On generated coherent systems and a conjecture of D. C. Butler Open
Let $(E,V)$ be a general generated coherent system of type $(n,d,n+m)$ on a general non-singular irreducible complex projective curve. A conjecture of D. C. Butler relates the semistability of $E$ to the semistability of the kernel of the …
View article: Higher rank BN-theory for curves of genus 6
Higher rank BN-theory for curves of genus 6 Open
Higher rank Brill-Noether theory for genus 6 is especially interesting as, even in the general case, some unexpected phenomena arise which are absent in lower genus. Moreover, it is the first case for which there exist curves of Clifford d…
View article: Higgs bundles over elliptic curves for real groups
Higgs bundles over elliptic curves for real groups Open
We study topologically trivial $G$-Higgs bundles over an elliptic curve $X$ when the structure group $G$ is a connected real form of a complex semisimple Lie group $G^{\mathbb{C}}$. We achieve a description of their (reduced) moduli space,…